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Homotopy Theory Of Schemes
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Book Synopsis Homotopy Theory of Schemes by : Fabien Morel
Download or read book Homotopy Theory of Schemes written by Fabien Morel and published by American Mathematical Soc.. This book was released on 2006 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this text, the author presents a general framework for applying the standard methods from homotopy theory to the category of smooth schemes over a reasonable base scheme $k$. He defines the homotopy category $h(\mathcal{E} k)$ of smooth $k$-schemes and shows that it plays the same role for smooth $k$-schemes as the classical homotopy category plays for differentiable varieties. It is shown that certain expected properties are satisfied, for example, concerning the algebraic$K$-theory of those schemes. In this way, advanced methods of algebraic topology become available in modern algebraic geometry.
Book Synopsis Etale Homotopy of Simplical Schemes by : Eric M. Friedlander
Download or read book Etale Homotopy of Simplical Schemes written by Eric M. Friedlander and published by Princeton University Press. This book was released on 1982-12-21 with total page 192 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.
Book Synopsis Motivic Homotopy Theory by : Bjorn Ian Dundas
Download or read book Motivic Homotopy Theory written by Bjorn Ian Dundas and published by Springer Science & Business Media. This book was released on 2007-07-11 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on lectures given at a summer school on motivic homotopy theory at the Sophus Lie Centre in Nordfjordeid, Norway, in August 2002. Aimed at graduate students in algebraic topology and algebraic geometry, it contains background material from both of these fields, as well as the foundations of motivic homotopy theory. It will serve as a good introduction as well as a convenient reference for a broad group of mathematicians to this important and fascinating new subject. Vladimir Voevodsky is one of the founders of the theory and received the Fields medal for his work, and the other authors have all done important work in the subject.
Book Synopsis Abstract Homotopy And Simple Homotopy Theory by : K Heiner Kamps
Download or read book Abstract Homotopy And Simple Homotopy Theory written by K Heiner Kamps and published by World Scientific. This book was released on 1997-04-11 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: The abstract homotopy theory is based on the observation that analogues of much of the topological homotopy theory and simple homotopy theory exist in many other categories (e.g. spaces over a fixed base, groupoids, chain complexes, module categories). Studying categorical versions of homotopy structure, such as cylinders and path space constructions, enables not only a unified development of many examples of known homotopy theories but also reveals the inner working of the classical spatial theory. This demonstrates the logical interdependence of properties (in particular the existence of certain Kan fillers in associated cubical sets) and results (Puppe sequences, Vogt's Iemma, Dold's theorem on fibre homotopy equivalences, and homotopy coherence theory).
Book Synopsis A1-homotopy Theory of Schemes by : Fabien Morel
Download or read book A1-homotopy Theory of Schemes written by Fabien Morel and published by . This book was released on 1999 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Simplicial Homotopy Theory by : Paul G. Goerss
Download or read book Simplicial Homotopy Theory written by Paul G. Goerss and published by Birkhäuser. This book was released on 2012-12-06 with total page 520 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.
Book Synopsis Introduction to Homotopy Theory by : Paul Selick
Download or read book Introduction to Homotopy Theory written by Paul Selick and published by American Mathematical Soc.. This book was released on 2008 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers a summary for students and non-specialists who are interested in learning the basics of algebraic topology. This book covers fibrations and cofibrations, Hurewicz and cellular approximation theorems, topics in classical homotopy theory, simplicial sets, fiber bundles, Hopf algebras, and generalized homology and cohomology operations.
Book Synopsis Etale Homotopy of Simplicial Schemes by : Eric M. Friedlander
Download or read book Etale Homotopy of Simplicial Schemes written by Eric M. Friedlander and published by . This book was released on 1982 with total page 190 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.
Download or read book Etale Homotopy written by Michael Artin and published by Springer. This book was released on 2006-11-14 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Homotopy Theory written by and published by Academic Press. This book was released on 1959-01-01 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: Homotopy Theory
Book Synopsis Homotopy Theory and Arithmetic Geometry – Motivic and Diophantine Aspects by : Frank Neumann
Download or read book Homotopy Theory and Arithmetic Geometry – Motivic and Diophantine Aspects written by Frank Neumann and published by Springer Nature. This book was released on 2021-09-29 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to state-of-the-art applications of homotopy theory to arithmetic geometry. The contributions to this volume are based on original lectures by leading researchers at the LMS-CMI Research School on ‘Homotopy Theory and Arithmetic Geometry - Motivic and Diophantine Aspects’ and the Nelder Fellow Lecturer Series, which both took place at Imperial College London in the summer of 2018. The contribution by Brazelton, based on the lectures by Wickelgren, provides an introduction to arithmetic enumerative geometry, the notes of Cisinski present motivic sheaves and new cohomological methods for intersection theory, and Schlank’s contribution gives an overview of the use of étale homotopy theory for obstructions to the existence of rational points on algebraic varieties. Finally, the article by Asok and Østvær, based in part on the Nelder Fellow lecture series by Østvær, gives a survey of the interplay between motivic homotopy theory and affine algebraic geometry, with a focus on contractible algebraic varieties. Now a major trend in arithmetic geometry, this volume offers a detailed guide to the fascinating circle of recent applications of homotopy theory to number theory. It will be invaluable to research students entering the field, as well as postdoctoral and more established researchers.
Book Synopsis The Geometry of Schemes by : David Eisenbud
Download or read book The Geometry of Schemes written by David Eisenbud and published by Springer Science & Business Media. This book was released on 2006-04-06 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: Grothendieck’s beautiful theory of schemes permeates modern algebraic geometry and underlies its applications to number theory, physics, and applied mathematics. This simple account of that theory emphasizes and explains the universal geometric concepts behind the definitions. In the book, concepts are illustrated with fundamental examples, and explicit calculations show how the constructions of scheme theory are carried out in practice.
Book Synopsis Homotopy Invariant Algebraic Structures by : Jean-Pierre Meyer
Download or read book Homotopy Invariant Algebraic Structures written by Jean-Pierre Meyer and published by American Mathematical Soc.. This book was released on 1999 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the proceedings of the conference held in honor of J. Michael Boardman's 60th birthday. It brings into print his classic work on conditionally convergent spectral sequences. Over the past 30 years, it has become evident that some of the deepest questions in algebra are best understood against the background of homotopy theory. Boardman and Vogt's theory of homotopy-theoretic algebraic structures and the theory of spectra, for example, were two benchmark breakthroughs underlying the development of algebraic $K$-theory and the recent advances in the theory of motives. The volume begins with short notes by Mac Lane, May, Stasheff, and others on the early and recent history of the subject. But the bulk of the volume consists of research papers on topics that have been strongly influenced by Boardman's work. Articles give readers a vivid sense of the current state of the theory of "homotopy-invariant algebraic structures". Also included are two major foundational papers by Goerss and Strickland on applications of methods of algebra (i.e., Dieudonné modules and formal schemes) to problems of topology. Boardman is known for the depth and wit of his ideas. This volume is intended to reflect and to celebrate those fine characteristics.
Book Synopsis Motives and Homotopy Theory of Schemes by : Mathematisches Forschungsinstitut Oberwolfach
Download or read book Motives and Homotopy Theory of Schemes written by Mathematisches Forschungsinstitut Oberwolfach and published by . This book was released on 2004 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Homotopy Theory and Models by : Marc Aubry
Download or read book Homotopy Theory and Models written by Marc Aubry and published by Springer Science & Business Media. This book was released on 1995-03-27 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: In keeping with the general aim of the "D.M.V.-Seminar" series, this book is princi pally a report on a group of lectures held at Blaubeuren by Professors H. J. Baues, S. Halperin and J.-M. Lemaire, from October 30 to November 7, 1988. These lec tures were devoted to providing an introduction to the theory of models in algebraic homotopy. The three lecturers acted in concert to produce a coherent exposition of the theory. Commencing from a common starting point, each of them then proceeded naturally to his own subject of research. The reader who is already familiar with their scientific work will certainly give the lecturers their due. Having been asked by the speakers to take on the responsibility of writing down the notes, it seemed to me that the material elucidated in the short span of fifteen hours was too dense to appear, unedited, in book form. Some amplification was necessary. Of course I submitted to them the final version of this book, which received their approval. I thank them for this token of confidence. I am also grateful to all three for their help and advice in writing this book. I am particularly indebted to J.-M. Lemaire who was indeed very often consulted. For basic notions (in particular those concerning homotopy groups, CW complexes, (co)homology and homological algebra) the reader is advised to refer to the fundamental books written by E. H. Spanier [47], R. M. Switzer [49] and G. Whitehead [52].
Book Synopsis Handbook of Homotopy Theory by : Haynes Miller
Download or read book Handbook of Homotopy Theory written by Haynes Miller and published by . This book was released on 2024-10-14 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Homotopy established the state-of-the-art research on this emerging topic in topology. The list of topics and contributors is impressive. The topics cover a broad swath, and the contributors will do an outstanding job. Students particularly will findthis book to be an entree to an active field of study.
Book Synopsis Primary Homotopy Theory by : Joseph Neisendorfer
Download or read book Primary Homotopy Theory written by Joseph Neisendorfer and published by American Mathematical Soc.. This book was released on 1980 with total page 73 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author gives a systematic exposition of homotopy groups with coefficients in a cyclic group [italic]Z or [italic]Z[subscript italic]k. The text pays particular attention to low-dimensional cases and trouble with the small primes. The book gives a complete treatment of some topics--such as Samelson products--with a view toward applications.
