Homotopical Algebraic Geometry Ii Geometric Stacks And Applications

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Homotopical Algebraic Geometry II: Geometric Stacks and Applications

Author : Bertrand Toen
Publisher : American Mathematical Soc.
ISBN 13 : 0821840991
Total Pages : 242 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Homotopical Algebraic Geometry II: Geometric Stacks and Applications by : Bertrand Toen

Download or read book Homotopical Algebraic Geometry II: Geometric Stacks and Applications written by Bertrand Toen and published by American Mathematical Soc.. This book was released on 2008 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second part of a series of papers called "HAG", devoted to developing the foundations of homotopical algebraic geometry. The authors start by defining and studying generalizations of standard notions of linear algebra in an abstract monoidal model category, such as derivations, étale and smooth morphisms, flat and projective modules, etc. They then use their theory of stacks over model categories to define a general notion of geometric stack over a base symmetric monoidal model category $C$, and prove that this notion satisfies the expected properties.

Homotopical Algebraic Geometry II

Author : Bertrand Toën
Publisher :
ISBN 13 : 9781470405083
Total Pages : 242 pages
Book Rating : 4.4/5 (5 download)

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Book Synopsis Homotopical Algebraic Geometry II by : Bertrand Toën

Download or read book Homotopical Algebraic Geometry II written by Bertrand Toën and published by . This book was released on 2014-09-11 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors start by defining and studying generalizations of standard notions of linear algebra in an abstract monoidal model category. They then use their theory of stacks over model categories to define a general notion of geometric stack over a base symmetric monoidal model category.

Algebraic Geometry

Author : Dan Abramovich
Publisher : American Mathematical Soc.
ISBN 13 : 0821847023
Total Pages : 506 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Algebraic Geometry by : Dan Abramovich

Download or read book Algebraic Geometry written by Dan Abramovich and published by American Mathematical Soc.. This book was released on 2009 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains research and expository papers by some of the speakers at the 2005 AMS Summer Institute on Algebraic Geometry. Numerous papers delve into the geometry of various moduli spaces, including those of stable curves, stable maps, coherent sheaves, and abelian varieties.

Algebraic Geometry over C∞-Rings

Author : Dominic Joyce
Publisher : American Mathematical Soc.
ISBN 13 : 1470436450
Total Pages : 139 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Algebraic Geometry over C∞-Rings by : Dominic Joyce

Download or read book Algebraic Geometry over C∞-Rings written by Dominic Joyce and published by American Mathematical Soc.. This book was released on 2019-09-05 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: If X is a manifold then the R-algebra C∞(X) of smooth functions c:X→R is a C∞-ring. That is, for each smooth function f:Rn→R there is an n-fold operation Φf:C∞(X)n→C∞(X) acting by Φf:(c1,…,cn)↦f(c1,…,cn), and these operations Φf satisfy many natural identities. Thus, C∞(X) actually has a far richer structure than the obvious R-algebra structure. The author explains the foundations of a version of algebraic geometry in which rings or algebras are replaced by C∞-rings. As schemes are the basic objects in algebraic geometry, the new basic objects are C∞-schemes, a category of geometric objects which generalize manifolds and whose morphisms generalize smooth maps. The author also studies quasicoherent sheaves on C∞-schemes, and C∞-stacks, in particular Deligne-Mumford C∞-stacks, a 2-category of geometric objects generalizing orbifolds. Many of these ideas are not new: C∞-rings and C∞ -schemes have long been part of synthetic differential geometry. But the author develops them in new directions. In earlier publications, the author used these tools to define d-manifolds and d-orbifolds, “derived” versions of manifolds and orbifolds related to Spivak's “derived manifolds”.

Homotopy Theory and Arithmetic Geometry – Motivic and Diophantine Aspects

Author : Frank Neumann
Publisher : Springer Nature
ISBN 13 : 3030789772
Total Pages : 223 pages
Book Rating : 4.0/5 (37 download)

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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.

Simplicial Methods for Operads and Algebraic Geometry

Author : Ieke Moerdijk
Publisher : Springer Science & Business Media
ISBN 13 : 3034800525
Total Pages : 186 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Simplicial Methods for Operads and Algebraic Geometry by : Ieke Moerdijk

Download or read book Simplicial Methods for Operads and Algebraic Geometry written by Ieke Moerdijk and published by Springer Science & Business Media. This book was released on 2010-12-01 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book is an introduction to two higher-categorical topics in algebraic topology and algebraic geometry relying on simplicial methods. It is based on lectures delivered at the Centre de Recerca Matemàtica in February 2008, as part of a special year on Homotopy Theory and Higher Categories"--Foreword

Stacks and Categories in Geometry, Topology, and Algebra

Author : Tony Pantev
Publisher : American Mathematical Soc.
ISBN 13 : 1470415577
Total Pages : 323 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Stacks and Categories in Geometry, Topology, and Algebra by : Tony Pantev

Download or read book Stacks and Categories in Geometry, Topology, and Algebra written by Tony Pantev and published by American Mathematical Soc.. This book was released on 2015-06-26 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the CATS4 Conference on Higher Categorical Structures and their Interactions with Algebraic Geometry, Algebraic Topology and Algebra, held from July 2-7, 2012, at CIRM in Luminy, France. Over the past several years, the CATS conference series has brought together top level researchers from around the world interested in relative and higher category theory and its applications to classical mathematical domains. Included in this volume is a collection of articles covering the applications of categories and stacks to geometry, topology and algebra. Techniques such as localization, model categories, simplicial objects, sheaves of categories, mapping stacks, dg structures, hereditary categories, and derived stacks, are applied to give new insight on cluster algebra, Lagrangians, trace theories, loop spaces, structured surfaces, stability, ind-coherent complexes and 1-affineness showing up in geometric Langlands, branching out to many related topics along the way.

Derived Algebraic Geometry

Author : Renaud Gauthier
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 311133421X
Total Pages : 489 pages
Book Rating : 4.1/5 (113 download)

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Book Synopsis Derived Algebraic Geometry by : Renaud Gauthier

Download or read book Derived Algebraic Geometry written by Renaud Gauthier and published by Walter de Gruyter GmbH & Co KG. This book was released on 2024-01-29 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mexican Mathematicians Abroad

Author : Noé Bárcenas
Publisher : American Mathematical Soc.
ISBN 13 : 1470421925
Total Pages : 237 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Mexican Mathematicians Abroad by : Noé Bárcenas

Download or read book Mexican Mathematicians Abroad written by Noé Bárcenas and published by American Mathematical Soc.. This book was released on 2016-02-01 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the First Workshop “Matemáticos Mexicanos Jóvenes en el Mundo”, held from August 22–24, 2012, at Centro de Investigación en Matemáticas (CIMAT) in Guanajuato, Mexico. - See more at: http://bookstore.ams.org/conm-657/#sthash.cUjwTcvX.dpuf This volume contains the proceedings of the First Workshop "Matemáticos Mexicanos Jóvenes en el Mundo", held from August 22-24, 2012, at Centro de Investigación en Matemáticas (CIMAT) in Guanajuato, Mexico. One of the main goals of this meeting was to present different research directions being pursued by young Mexican mathematicians based in other countries, such as Brazil, Canada, Colombia, Estonia, Germany, Spain and the United States, showcasing research lines currently underrepresented in Mexico. Featured are survey and research articles in six areas: algebra, analysis, applied mathematics, geometry, probability and topology. Their topics range from current developments related to well-known open problems to novel interactions between pure mathematics and computer science. Most of the articles provide a panoramic view of the fields and problems the authors work on, making the book accessible to advanced graduate students and researchers in mathematics from different fields. This book is published in cooperation with Sociedad Matemática Mexicana.

Geometry, Analysis and Probability

Author : Jean-Benoît Bost
Publisher : Birkhäuser
ISBN 13 : 3319496387
Total Pages : 361 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis Geometry, Analysis and Probability by : Jean-Benoît Bost

Download or read book Geometry, Analysis and Probability written by Jean-Benoît Bost and published by Birkhäuser. This book was released on 2017-04-26 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents original research articles and extended surveys related to the mathematical interest and work of Jean-Michel Bismut. His outstanding contributions to probability theory and global analysis on manifolds have had a profound impact on several branches of mathematics in the areas of control theory, mathematical physics and arithmetic geometry. Contributions by: K. Behrend N. Bergeron S. K. Donaldson J. Dubédat B. Duplantier G. Faltings E. Getzler G. Kings R. Mazzeo J. Millson C. Moeglin W. Müller R. Rhodes D. Rössler S. Sheffield A. Teleman G. Tian K-I. Yoshikawa H. Weiss W. Werner The collection is a valuable resource for graduate students and researchers in these fields.

C?-Algebraic Geometry with Corners

Author : Kelli Francis-Staite
Publisher : Cambridge University Press
ISBN 13 : 1009400169
Total Pages : 223 pages
Book Rating : 4.0/5 (94 download)

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Book Synopsis C?-Algebraic Geometry with Corners by : Kelli Francis-Staite

Download or read book C?-Algebraic Geometry with Corners written by Kelli Francis-Staite and published by Cambridge University Press. This book was released on 2023-12-31 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: Crossing the boundary between differential and algebraic geometry in order to study singular spaces, this book introduces 'C∞-schemes with corners'.

Mathematical Aspects of Quantum Field Theories

Author : Damien Calaque
Publisher : Springer
ISBN 13 : 3319099493
Total Pages : 556 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Mathematical Aspects of Quantum Field Theories by : Damien Calaque

Download or read book Mathematical Aspects of Quantum Field Theories written by Damien Calaque and published by Springer. This book was released on 2015-01-06 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: Despite its long history and stunning experimental successes, the mathematical foundation of perturbative quantum field theory is still a subject of ongoing research. This book aims at presenting some of the most recent advances in the field, and at reflecting the diversity of approaches and tools invented and currently employed. Both leading experts and comparative newcomers to the field present their latest findings, helping readers to gain a better understanding of not only quantum but also classical field theories. Though the book offers a valuable resource for mathematicians and physicists alike, the focus is more on mathematical developments. This volume consists of four parts: The first Part covers local aspects of perturbative quantum field theory, with an emphasis on the axiomatization of the algebra behind the operator product expansion. The second Part highlights Chern-Simons gauge theories, while the third examines (semi-)classical field theories. In closing, Part 4 addresses factorization homology and factorization algebras.

Infinity Properads and Infinity Wheeled Properads

Author : Philip Hackney
Publisher : Springer
ISBN 13 : 3319205471
Total Pages : 358 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Infinity Properads and Infinity Wheeled Properads by : Philip Hackney

Download or read book Infinity Properads and Infinity Wheeled Properads written by Philip Hackney and published by Springer. This book was released on 2015-09-07 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: The topic of this book sits at the interface of the theory of higher categories (in the guise of (∞,1)-categories) and the theory of properads. Properads are devices more general than operads and enable one to encode bialgebraic, rather than just (co)algebraic, structures. The text extends both the Joyal-Lurie approach to higher categories and the Cisinski-Moerdijk-Weiss approach to higher operads, and provides a foundation for a broad study of the homotopy theory of properads. This work also serves as a complete guide to the generalised graphs which are pervasive in the study of operads and properads. A preliminary list of potential applications and extensions comprises the final chapter. Infinity Properads and Infinity Wheeled Properads is written for mathematicians in the fields of topology, algebra, category theory, and related areas. It is written roughly at the second year graduate level, and assumes a basic knowledge of category theory.

The Geometry, Topology And Physics Of Moduli Spaces Of Higgs Bundles

Author : Richard Wentworth
Publisher : World Scientific
ISBN 13 : 9813229101
Total Pages : 412 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis The Geometry, Topology And Physics Of Moduli Spaces Of Higgs Bundles by : Richard Wentworth

Download or read book The Geometry, Topology And Physics Of Moduli Spaces Of Higgs Bundles written by Richard Wentworth and published by World Scientific. This book was released on 2018-06-28 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the 25 years since their introduction, Higgs bundles have seen a surprising number of interactions within different areas of mathematics and physics. There is a recent surge of interest following Ngô Bau Châu's proof of the Fundamental Lemma and the work of Kapustin and Witten on the Geometric Langlands program. The program on The Geometry, Topology and Physics of Moduli Spaces of Higgs Bundles, was held at the Institute for Mathematical Sciences at the National University of Singapore during 2014. It hosted a number of lectures on recent topics of importance related to Higgs bundles, and it is the purpose of this volume to collect these lectures in a form accessible to graduate students and young researchers interested in learning more about this field.

A Handbook of Model Categories

Author : Scott Balchin
Publisher : Springer Nature
ISBN 13 : 3030750353
Total Pages : 326 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis A Handbook of Model Categories by : Scott Balchin

Download or read book A Handbook of Model Categories written by Scott Balchin and published by Springer Nature. This book was released on 2021-10-29 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Algebra, Geometry, and Physics in the 21st Century

Author : Denis Auroux
Publisher : Birkhäuser
ISBN 13 : 3319599399
Total Pages : 364 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Algebra, Geometry, and Physics in the 21st Century by : Denis Auroux

Download or read book Algebra, Geometry, and Physics in the 21st Century written by Denis Auroux and published by Birkhäuser. This book was released on 2017-07-27 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a tribute to Maxim Kontsevich, one of the most original and influential mathematicians of our time. Maxim’s vision has inspired major developments in many areas of mathematics, ranging all the way from probability theory to motives over finite fields, and has brought forth a paradigm shift at the interface of modern geometry and mathematical physics. Many of his papers have opened completely new directions of research and led to the solutions of many classical problems. This book collects papers by leading experts currently engaged in research on topics close to Maxim’s heart. Contributors: S. Donaldson A. Goncharov D. Kaledin M. Kapranov A. Kapustin L. Katzarkov A. Noll P. Pandit S. Pimenov J. Ren P. Seidel C. Simpson Y. Soibelman R. Thorngren

Handbook of Homotopy Theory

Author : Haynes Miller
Publisher : CRC Press
ISBN 13 : 1351251600
Total Pages : 1043 pages
Book Rating : 4.3/5 (512 download)

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Book Synopsis Handbook of Homotopy Theory by : Haynes Miller

Download or read book Handbook of Homotopy Theory written by Haynes Miller and published by CRC Press. This book was released on 2020-01-23 with total page 1043 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.