Download Generalized Etale Cohomology Theories PDF Full

Generalized Etale Cohomology Theories

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Publisher : Springer Science & Business Media
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ISBN : 3034800657
Pages : 317 pages
Rating : 4.4/5 (8 Download)

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Download Free Generalized Etale Cohomology Theories PDF by John Jardine Full Book and published by Springer Science & Business Media. This book was released on 2010-12-15 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: A generalized etale cohomology theory is a theory which is represented by a presheaf of spectra on an etale site for an algebraic variety, in analogy with the way an ordinary spectrum represents a cohomology theory for spaces. Examples include etale cohomology and etale K-theory. This book gives new and complete proofs of both Thomason's descent theorem for Bott periodic K-theory and the Nisnevich descent theorem. In doing so, it exposes most of the major ideas of the homotopy theory of presheaves of spectra, and generalized etale homology theories in particular. The treatment includes, for the purpose of adequately dealing with cup product structures, a development of stable homotopy theory for n-fold spectra, which is then promoted to the level of presheaves of n-fold spectra. This book should be of interest to all researchers working in fields related to algebraic K-theory. The techniques presented here are essentially combinatorial, and hence algebraic. An extensive background in traditional stable homotopy theory is not assumed. ------ Reviews (...) in developing the techniques of the subject, introduces the reader to the stable homotopy category of simplicial presheaves. (...) This book provides the user with the first complete account which is sensitive enough to be compatible with the sort of closed model category necessary in K-theory applications (...). As an application of the techniques the author gives proofs of the descent theorems of R. W. Thomason and Y. A. Nisnevich. (...) The book concludes with a discussion of the Lichtenbaum-Quillen conjecture (an approximation to Thomason’s theorem without Bott periodicity). The recent proof of this conjecture, by V. Voevodsky, (...) makes this volume compulsory reading for all who want to be au fait with current trends in algebraic K-theory! - Zentralblatt MATH The presentation of these topics is highly original. The book will be very useful for any researcher interested in subjects related to algebraic K-theory. - Matematica

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Generalized Cohomology

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Publisher : American Mathematical Soc.
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ISBN : 9780821835142
Pages : 254 pages
Rating : 4.5/5 (149 Download)

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Download Free Generalized Cohomology PDF by Akira Kono Full Book and published by American Mathematical Soc.. This book was released on 2006 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aims to give an exposition of generalized (co)homology theories that can be read by a group of mathematicians who are not experts in algebraic topology. This title starts with basic notions of homotopy theory, and introduces the axioms of generalized (co)homology theory. It also discusses various types of generalized cohomology theories.

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Axiomatic, Enriched and Motivic Homotopy Theory

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Publisher : Springer Science & Business Media
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ISBN : 940070948X
Pages : 392 pages
Rating : 4.0/5 (79 Download)

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Download Free Axiomatic, Enriched and Motivic Homotopy Theory PDF by John Greenlees Full Book and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: The NATO Advanced Study Institute "Axiomatic, enriched and rna tivic homotopy theory" took place at the Isaac Newton Institute of Mathematical Sciences, Cambridge, England during 9-20 September 2002. The Directors were J.P.C.Greenlees and I.Zhukov; the other or ganizers were P.G.Goerss, F.Morel, J.F.Jardine and V.P.Snaith. The title describes the content well, and both the event and the contents of the present volume reflect recent remarkable successes in model categor ies, structured ring spectra and homotopy theory of algebraic geometry. The ASI took the form of a series of 15 minicourses and a few extra lectures, and was designed to provide background, and to bring the par ticipants up to date with developments. The present volume is based on a number of the lectures given during the workshop. The ASI was the opening workshop of the four month programme "New Contexts for Stable Homotopy Theory" which explored several themes in greater depth. I am grateful to the Isaac Newton Institute for providing such an ideal venue, the NATO Science Committee for their funding, and to all the speakers at the conference, whether or not they were able to contribute to the present volume. All contributions were refereed, and I thank the authors and referees for their efforts to fit in with the tight schedule. Finally, I would like to thank my coorganizers and all the staff at the Institute for making the ASI run so smoothly. J.P.C.GREENLEES.

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Canadian Mathematical Bulletin

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Pages : 132 pages
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Download Free Canadian Mathematical Bulletin PDF by Full Book and published by . This book was released on 1993-12 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download Handbook of K-Theory PDF Full

Handbook of K-Theory

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Publisher : Springer Science & Business Media
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ISBN : 354023019X
Pages : 626 pages
Rating : 4.0/5 (23 Download)

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Download Free Handbook of K-Theory PDF by Eric Friedlander Full Book and published by Springer Science & Business Media. This book was released on 2005-07-18 with total page 626 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook offers a compilation of techniques and results in K-theory. Each chapter is dedicated to a specific topic and is written by a leading expert. Many chapters present historical background; some present previously unpublished results, whereas some present the first expository account of a topic; many discuss future directions as well as open problems. It offers an exposition of our current state of knowledge as well as an implicit blueprint for future research.

Download Homotopy Theory: Tools and Applications PDF Full

Homotopy Theory: Tools and Applications

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Publisher : American Mathematical Soc.
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ISBN : 1470442442
Pages : 268 pages
Rating : 4.0/5 (442 Download)

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Download Free Homotopy Theory: Tools and Applications PDF by Daniel G. Davis Full Book and published by American Mathematical Soc.. This book was released on 2019-05-30 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the conference Homotopy Theory: Tools and Applications, in honor of Paul Goerss's 60th birthday, held from July 17–21, 2017, at the University of Illinois at Urbana-Champaign, Urbana, IL. The articles cover a variety of topics spanning the current research frontier of homotopy theory. This includes articles concerning both computations and the formal theory of chromatic homotopy, different aspects of equivariant homotopy theory and K-theory, as well as articles concerned with structured ring spectra, cyclotomic spectra associated to perfectoid fields, and the theory of higher homotopy operations.

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Simplicial Homotopy Theory

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Publisher : Birkhäuser
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ISBN : 3034887078
Pages : 510 pages
Rating : 4.4/5 (887 Download)

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Download Free Simplicial Homotopy Theory PDF by Paul G. Goerss Full Book and published by Birkhäuser. This book was released on 2012-12-06 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the beginning of the modern era of algebraic topology, simplicial methods have been used systematically and effectively for both computation and basic theory. With the development of Quillen's concept of a closed model category and, in particular, a simplicial model category, this collection of methods has become the primary way to describe non-abelian homological algebra and to address homotopy-theoretical issues in a variety of fields, including algebraic K-theory. This book supplies a modern exposition of these ideas, emphasizing model category theoretical techniques. Discussed here are the homotopy theory of simplicial sets, and other basic topics such as simplicial groups, Postnikov towers, and bisimplicial sets. The more advanced material includes homotopy limits and colimits, localization with respect to a map and with respect to a homology theory, cosimplicial spaces, and homotopy coherence. Interspersed throughout are many results and ideas well-known to experts, but uncollected in the literature. Intended for second-year graduate students and beyond, this book introduces many of the basic tools of modern homotopy theory. An extensive background in topology is not assumed.

Download Etale Homotopy of Simplicial Schemes. (AM-104), Volume 104 PDF Full

Etale Homotopy of Simplicial Schemes. (AM-104), Volume 104

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Publisher : Princeton University Press
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ISBN : 1400881498
Pages : 191 pages
Rating : 4.0/5 (881 Download)

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Download Free Etale Homotopy of Simplicial Schemes. (AM-104), Volume 104 PDF by Eric M. Friedlander Full Book and published by Princeton University Press. This book was released on 2016-03-02 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a coherent account of the current status of etale homotopy theory, a topological theory introduced into abstract algebraic geometry by M. Artin and B. Mazur. Eric M. Friedlander presents many of his own applications of this theory to algebraic topology, finite Chevalley groups, and algebraic geometry. Of particular interest are the discussions concerning the Adams Conjecture, K-theories of finite fields, and Poincare duality. Because these applications have required repeated modifications of the original formulation of etale homotopy theory, the author provides a new treatment of the foundations which is more general and more precise than previous versions. One purpose of this book is to offer the basic techniques and results of etale homotopy theory to topologists and algebraic geometers who may then apply the theory in their own work. With a view to such future applications, the author has introduced a number of new constructions (function complexes, relative homology and cohomology, generalized cohomology) which have immediately proved applicable to algebraic K-theory.

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Local Homotopy Theory

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Publisher : Springer
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ISBN : 1493923005
Pages : 508 pages
Rating : 4.3/5 (923 Download)

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Download Free Local Homotopy Theory PDF by John F. Jardine Full Book and published by Springer. This book was released on 2015-05-27 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph on the homotopy theory of topologized diagrams of spaces and spectra gives an expert account of a subject at the foundation of motivic homotopy theory and the theory of topological modular forms in stable homotopy theory. Beginning with an introduction to the homotopy theory of simplicial sets and topos theory, the book covers core topics such as the unstable homotopy theory of simplicial presheaves and sheaves, localized theories, cocycles, descent theory, non-abelian cohomology, stacks, and local stable homotopy theory. A detailed treatment of the formalism of the subject is interwoven with explanations of the motivation, development, and nuances of ideas and results. The coherence of the abstract theory is elucidated through the use of widely applicable tools, such as Barr's theorem on Boolean localization, model structures on the category of simplicial presheaves on a site, and cocycle categories. A wealth of concrete examples convey the vitality and importance of the subject in topology, number theory, algebraic geometry, and algebraic K-theory. Assuming basic knowledge of algebraic geometry and homotopy theory, Local Homotopy Theory will appeal to researchers and advanced graduate students seeking to understand and advance the applications of homotopy theory in multiple areas of mathematics and the mathematical sciences.

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Structured Ring Spectra

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Publisher : Cambridge University Press
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ISBN : 9780521603058
Pages : 236 pages
Rating : 4.3/5 (56 Download)

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Download Free Structured Ring Spectra PDF by Andrew Baker Full Book and published by Cambridge University Press. This book was released on 2004-11-18 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains some important new contributions to the theory of structured ring spectra.

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Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics

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Publisher : Springer
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ISBN : 3319968270
Pages : 604 pages
Rating : 4.9/5 (968 Download)

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Download Free Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics PDF by Gert-Martin Greuel Full Book and published by Springer. This book was released on 2018-09-18 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume brings together recent, original research and survey articles by leading experts in several fields that include singularity theory, algebraic geometry and commutative algebra. The motivation for this collection comes from the wide-ranging research of the distinguished mathematician, Antonio Campillo, in these and related fields. Besides his influence in the mathematical community stemming from his research, Campillo has also endeavored to promote mathematics and mathematicians' networking everywhere, especially in Spain, Latin America and Europe. Because of his impressive achievements throughout his career, we dedicate this book to Campillo in honor of his 65th birthday. Researchers and students from the world-wide, and in particular Latin American and European, communities in singularities, algebraic geometry, commutative algebra, coding theory, and other fields covered in the volume, will have interest in this book.

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Stable Homotopy Around the Arf-Kervaire Invariant

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Publisher : Springer Science & Business Media
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ISBN : 376439904X
Pages : 239 pages
Rating : 4.4/5 (399 Download)

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Download Free Stable Homotopy Around the Arf-Kervaire Invariant PDF by Victor P. Snaith Full Book and published by Springer Science & Business Media. This book was released on 2009-03-28 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: Were I to take an iron gun, And ?re it o? towards the sun; I grant ‘twould reach its mark at last, But not till many years had passed. But should that bullet change its force, And to the planets take its course, ‘Twould never reach the nearest star, Because it is so very far. from FACTS by Lewis Carroll [55] Let me begin by describing the two purposes which prompted me to write this monograph. This is a book about algebraic topology and more especially about homotopy theory. Since the inception of algebraic topology [217] the study of homotopy classes of continuous maps between spheres has enjoyed a very exc- n n tional, central role. As is well known, for homotopy classes of maps f : S ?? S with n? 1 the sole homotopy invariant is the degree, which characterises the homotopy class completely. The search for a continuous map between spheres of di?erent dimensions and not homotopic to the constant map had to wait for its resolution until the remarkable paper of Heinz Hopf [111]. In retrospect, ?nding 3 an example was rather easy because there is a canonical quotient map from S to 3 1 1 2 theorbitspaceofthe freecircleactionS /S =CP = S .

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Algebraic K-theory

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Publisher : American Mathematical Soc.
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ISBN : 0821805118
Pages : 210 pages
Rating : 4.1/5 (85 Download)

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Download Free Algebraic K-theory PDF by Grzegorz Banaszak Full Book and published by American Mathematical Soc.. This book was released on 1996 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains proceedings of the research conference on algebraic $K$-theory that took place in Poznan, Poland, in September 1995. The conference concluded the activity of the algebraic $K$-theory seminar held at the Adam Mickiewicz University in the academic year 1994-1995. Talks at the conference covered a wide range of current research activities in algebraic $K$-theory. In particular, the following topics were covered: $K$-theory of fields and rings of integers; $K$-theory of elliptic and modular curves; theory of motives, motivic cohomology, Beilinson conjectures; and, algebraic $K$-theory of topological spaces, topological Hochschild homology and cyclic homology. With contributions by some leading experts in the field, this book provides a look at the state of current research in algebraic $K$-theory.

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Module Theory

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Publisher : Springer Science & Business Media
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ISBN : 9783764359089
Pages : 288 pages
Rating : 4.9/5 (8 Download)

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Download Free Module Theory PDF by Alberto Facchini Full Book and published by Springer Science & Business Media. This book was released on 1998-06-16 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This expository monograph was written for three reasons. Firstly, we wanted to present the solution to a problem posed by Wolfgang Krull in 1932 [Krull 32]. He asked whether what we now call the "Krull-Schmidt Theorem" holds for ar tinian modules. The problem remained open for 63 years: its solution, a negative answer to Krull's question, was published only in 1995 (see [Facchini, Herbera, Levy and Vamos]). Secondly, we wanted to present the answer to a question posed by Warfield in 1975 [Warfield 75]. He proved that every finitely pre sented module over a serial ring is a direct sum of uniserial modules, and asked if such a decomposition was unique. In other words, Warfield asked whether the "Krull-Schmidt Theorem" holds for serial modules. The solution to this problem, a negative answer again, appeared in [Facchini 96]. Thirdly, the so lution to Warfield's problem shows interesting behavior, a rare phenomenon in the history of Krull-Schmidt type theorems. Essentially, the Krull-Schmidt Theorem holds for some classes of modules and not for others. When it does hold, any two indecomposable decompositions are uniquely determined up to a permutation, and when it does not hold for a class of modules, this is proved via an example. For serial modules the Krull-Schmidt Theorem does not hold, but any two indecomposable decompositions are uniquely determined up to two permutations. We wanted to present such a phenomenon to a wider math ematical audience.

Download Elements of the Representation Theory of the Jacobi Group PDF Full

Elements of the Representation Theory of the Jacobi Group

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Publisher : Springer Science & Business Media
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ISBN : 9783764359225
Pages : 213 pages
Rating : 4.9/5 (226 Download)

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Download Free Elements of the Representation Theory of the Jacobi Group PDF by Rolf Berndt Full Book and published by Springer Science & Business Media. This book was released on 1998 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Jacobi group is a semidirect product of a symplectic group with a Heisenberg group. It is an important example for a non-reductive group and sets the frame within which to treat theta functions as well as elliptic functions - in particular, the universal elliptic curve. This text gathers for the first time material from the representation theory of this group in both local (archimedean and non-archimedean) cases and in the global number field case. Via a bridge to Waldspurger's theory for the metaplectic group, complete classification theorems for irreducible representations are obtained. Further topics include differential operators, Whittaker models, Hecke operators, spherical representations and theta functions. The global theory is aimed at the correspondence between automorphic representations and Jacobi forms. This volume is thus a complement to the seminal book on Jacobi forms by M. Eichler and D. Zagier. Incorporating results of the authors' original research, this exposition is meant for researchers and graduate students interested in algebraic groups and number theory, in particular, modular and automorphic forms.

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A Tribute to C.S. Seshadri

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Publisher : Springer Science & Business Media
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ISBN : 9783764304447
Pages : 551 pages
Rating : 4.4/5 (448 Download)

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Download Free A Tribute to C.S. Seshadri PDF by Venkatrama Lakshmibai Full Book and published by Springer Science & Business Media. This book was released on 2003-07-24 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: C.S. Seshadri turned seventy on the 29th of February, 2002. To mark this occasion, a symposium was held in Chennai, India, where some of his colleagues gave expository talks highlighting Seshadri's contributions to mathematics. This volume includes expanded texts of these talks as well as research and expository papers on geometry and representation theory. It will serve as an excellent reference for researchers and students in these areas.

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Categorical Decomposition Techniques in Algebraic Topology

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Publisher : Springer Science & Business Media
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ISBN : 9783764304003
Pages : 304 pages
Rating : 4.4/5 (6 Download)

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Download Free Categorical Decomposition Techniques in Algebraic Topology PDF by Gregory Arone Full Book and published by Springer Science & Business Media. This book was released on 2003-11-27 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book consists of articles at the frontier of current research in Algebraic Topology. It presents recent results by top notch experts, and is intended primarily for researchers and graduate students working in the field of algebraic topology. Included is an important article by Cohen, Johnes and Yan on the homology of the space of smooth loops on a manifold M, endowed with the Chas-Sullivan intersection product, as well as an article by Goerss, Henn and Mahowald on stable homotopy groups of spheres, which uses the cutting edge technology of "topological modular forms".