Axiomatic Enriched And Motivic Homotopy Theory

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Axiomatic, Enriched and Motivic Homotopy Theory

Author : John Greenlees
Publisher : Springer Science & Business Media
Page : 396 pages
File Size : 48,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400709485

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Axiomatic, Enriched and Motivic Homotopy Theory by John Greenlees Pdf

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.

Motivic Homotopy Theory and Refined Enumerative Geometry

Author : Federico Binda,Marc Levine,Manh Toan Nguyen,Oliver Röndigs
Publisher : American Mathematical Soc.
Page : 267 pages
File Size : 54,6 Mb
Release : 2020-03-09
Category : Education
ISBN : 9781470448981

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Motivic Homotopy Theory and Refined Enumerative Geometry by Federico Binda,Marc Levine,Manh Toan Nguyen,Oliver Röndigs Pdf

This volume contains the proceedings of the Workshop on Motivic Homotopy Theory and Refined Enumerative Geometry, held from May 14–18, 2018, at the Universität Duisburg-Essen, Essen, Germany. It constitutes an accessible yet swift introduction to a new and active area within algebraic geometry, which connects well with classical intersection theory. Combining both lecture notes aimed at the graduate student level and research articles pointing towards the manifold promising applications of this refined approach, it broadly covers refined enumerative algebraic geometry.

Handbook of Homotopy Theory

Author : Haynes Miller
Publisher : CRC Press
Page : 1043 pages
File Size : 42,5 Mb
Release : 2020-01-23
Category : Mathematics
ISBN : 9781351251600

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Handbook of Homotopy Theory by Haynes Miller Pdf

The Handbook of Homotopy Theory provides a panoramic view of an active area in mathematics that is currently seeing dramatic solutions to long-standing open problems, and is proving itself of increasing importance across many other mathematical disciplines. The origins of the subject date back to work of Henri Poincaré and Heinz Hopf in the early 20th century, but it has seen enormous progress in the 21st century. A highlight of this volume is an introduction to and diverse applications of the newly established foundational theory of ¥ -categories. The coverage is vast, ranging from axiomatic to applied, from foundational to computational, and includes surveys of applications both geometric and algebraic. The contributors are among the most active and creative researchers in the field. The 22 chapters by 31 contributors are designed to address novices, as well as established mathematicians, interested in learning the state of the art in this field, whose methods are of increasing importance in many other areas.

Author : Anonim
Publisher : World Scientific
Page : 1191 pages
File Size : 54,6 Mb
Release : 2024-07-01
Category : Electronic
ISBN : 8210379456XXX

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by Anonim Pdf

Proceedings Of The International Congress Of Mathematicians 2010 (Icm 2010) (In 4 Volumes) - Vol. I: Plenary Lectures And Ceremonies, Vols. Ii-iv: Invited Lectures

Author : Bhatia Rajendra,Pal Arup,Rangarajan G
Publisher : World Scientific
Page : 4144 pages
File Size : 50,8 Mb
Release : 2011-06-06
Category : Mathematics
ISBN : 9789814462938

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Proceedings Of The International Congress Of Mathematicians 2010 (Icm 2010) (In 4 Volumes) - Vol. I: Plenary Lectures And Ceremonies, Vols. Ii-iv: Invited Lectures by Bhatia Rajendra,Pal Arup,Rangarajan G Pdf

ICM 2010 proceedings comprises a four-volume set containing articles based on plenary lectures and invited section lectures, the Abel and Noether lectures, as well as contributions based on lectures delivered by the recipients of the Fields Medal, the Nevanlinna, and Chern Prizes. The first volume will also contain the speeches at the opening and closing ceremonies and other highlights of the Congress.

Stable Homotopy Around the Arf-Kervaire Invariant

Author : Victor P. Snaith
Publisher : Springer Science & Business Media
Page : 250 pages
File Size : 53,8 Mb
Release : 2009-03-28
Category : Mathematics
ISBN : 9783764399047

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Stable Homotopy Around the Arf-Kervaire Invariant by Victor P. Snaith Pdf

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 .

Cubical Homotopy Theory

Author : Brian A. Munson,Ismar Volić
Publisher : Cambridge University Press
Page : 649 pages
File Size : 48,7 Mb
Release : 2015-10-06
Category : Mathematics
ISBN : 9781107030251

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Cubical Homotopy Theory by Brian A. Munson,Ismar Volić Pdf

A modern, example-driven introduction to cubical diagrams and related topics such as homotopy limits and cosimplicial spaces.

Introduction to Stable Homotopy Theory

Author : David Barnes,Constanze Roitzheim
Publisher : Cambridge University Press
Page : 431 pages
File Size : 50,8 Mb
Release : 2020-03-26
Category : Mathematics
ISBN : 9781108482783

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Introduction to Stable Homotopy Theory by David Barnes,Constanze Roitzheim Pdf

A comprehensive introduction to stable homotopy theory for beginning graduate students, from motivating phenomena to current research.

Bousfield Classes and Ohkawa's Theorem

Author : Takeo Ohsawa,Norihiko Minami
Publisher : Springer Nature
Page : 438 pages
File Size : 50,6 Mb
Release : 2020-03-18
Category : Mathematics
ISBN : 9789811515880

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Bousfield Classes and Ohkawa's Theorem by Takeo Ohsawa,Norihiko Minami Pdf

This volume originated in the workshop held at Nagoya University, August 28–30, 2015, focusing on the surprising and mysterious Ohkawa's theorem: the Bousfield classes in the stable homotopy category SH form a set. An inspiring, extensive mathematical story can be narrated starting with Ohkawa's theorem, evolving naturally with a chain of motivational questions: Ohkawa's theorem states that the Bousfield classes of the stable homotopy category SH surprisingly forms a set, which is still very mysterious. Are there any toy models where analogous Bousfield classes form a set with a clear meaning? The fundamental theorem of Hopkins, Neeman, Thomason, and others states that the analogue of the Bousfield classes in the derived category of quasi-coherent sheaves Dqc(X) form a set with a clear algebro-geometric description. However, Hopkins was actually motivated not by Ohkawa's theorem but by his own theorem with Smith in the triangulated subcategory SHc, consisting of compact objects in SH. Now the following questions naturally occur: (1) Having theorems of Ohkawa and Hopkins-Smith in SH, are there analogues for the Morel-Voevodsky A1-stable homotopy category SH(k), which subsumes SH when k is a subfield of C?, (2) Was it not natural for Hopkins to have considered Dqc(X)c instead of Dqc(X)? However, whereas there is a conceptually simple algebro-geometrical interpretation Dqc(X)c = Dperf(X), it is its close relative Dbcoh(X) that traditionally, ever since Oka and Cartan, has been intensively studied because of its rich geometric and physical information. This book contains developments for the rest of the story and much more, including the chromatics homotopy theory, which the Hopkins–Smith theorem is based upon, and applications of Lurie's higher algebra, all by distinguished contributors.

A Handbook of Model Categories

Author : Scott Balchin
Publisher : Springer Nature
Page : 326 pages
File Size : 51,9 Mb
Release : 2021-10-29
Category : Mathematics
ISBN : 9783030750350

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A Handbook of Model Categories by Scott Balchin Pdf

This book outlines a vast array of techniques and methods regarding model categories, without focussing on the intricacies of the proofs. Quillen model categories are a fundamental tool for the understanding of homotopy theory. While many introductions to model categories fall back on the same handful of canonical examples, the present book highlights a large, self-contained collection of other examples which appear throughout the literature. In particular, it collects a highly scattered literature into a single volume. The book is aimed at anyone who uses, or is interested in using, model categories to study homotopy theory. It is written in such a way that it can be used as a reference guide for those who are already experts in the field. However, it can also be used as an introduction to the theory for novices.

A1-Algebraic Topology over a Field

Author : Fabien Morel
Publisher : Springer
Page : 267 pages
File Size : 51,7 Mb
Release : 2012-07-13
Category : Mathematics
ISBN : 9783642295140

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A1-Algebraic Topology over a Field by Fabien Morel Pdf

This text deals with A1-homotopy theory over a base field, i.e., with the natural homotopy theory associated to the category of smooth varieties over a field in which the affine line is imposed to be contractible. It is a natural sequel to the foundational paper on A1-homotopy theory written together with V. Voevodsky. Inspired by classical results in algebraic topology, we present new techniques, new results and applications related to the properties and computations of A1-homotopy sheaves, A1-homology sheaves, and sheaves with generalized transfers, as well as to algebraic vector bundles over affine smooth varieties.

Triangulated Categories of Mixed Motives

Author : Denis-Charles Cisinski,Frédéric Déglise
Publisher : Springer Nature
Page : 406 pages
File Size : 46,5 Mb
Release : 2019-11-09
Category : Mathematics
ISBN : 9783030332426

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Triangulated Categories of Mixed Motives by Denis-Charles Cisinski,Frédéric Déglise Pdf

The primary aim of this monograph is to achieve part of Beilinson’s program on mixed motives using Voevodsky’s theories of A1-homotopy and motivic complexes. Historically, this book is the first to give a complete construction of a triangulated category of mixed motives with rational coefficients satisfying the full Grothendieck six functors formalism as well as fulfilling Beilinson’s program, in particular the interpretation of rational higher Chow groups as extension groups. Apart from Voevodsky’s entire work and Grothendieck’s SGA4, our main sources are Gabber’s work on étale cohomology and Ayoub’s solution to Voevodsky’s cross functors theory. We also thoroughly develop the theory of motivic complexes with integral coefficients over general bases, along the lines of Suslin and Voevodsky. Besides this achievement, this volume provides a complete toolkit for the study of systems of coefficients satisfying Grothendieck’ six functors formalism, including Grothendieck-Verdier duality. It gives a systematic account of cohomological descent theory with an emphasis on h-descent. It formalizes morphisms of coefficient systems with a view towards realization functors and comparison results. The latter allows to understand the polymorphic nature of rational mixed motives. They can be characterized by one of the following properties: existence of transfers, universality of rational algebraic K-theory, h-descent, étale descent, orientation theory. This monograph is a longstanding research work of the two authors. The first three parts are written in a self-contained manner and could be accessible to graduate students with a background in algebraic geometry and homotopy theory. It is designed to be a reference work and could also be useful outside motivic homotopy theory. The last part, containing the most innovative results, assumes some knowledge of motivic homotopy theory, although precise statements and references are given.

Mathematical Reviews

Author : Anonim
Publisher : Unknown
Page : 884 pages
File Size : 44,6 Mb
Release : 2007
Category : Mathematics
ISBN : UOM:39015076649873

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Mathematical Reviews by Anonim Pdf

The British National Bibliography

Author : Arthur James Wells
Publisher : Unknown
Page : 1382 pages
File Size : 44,8 Mb
Release : 2004
Category : Bibliography, National
ISBN : UOM:39015057956560

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The British National Bibliography by Arthur James Wells Pdf

St. Petersburg Mathematical Journal

Author : Anonim
Publisher : Unknown
Page : 642 pages
File Size : 50,5 Mb
Release : 2008
Category : Algebra
ISBN : UOM:39015072637195

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St. Petersburg Mathematical Journal by Anonim Pdf