Torsors Étale Homotopy And Applications To Rational Points

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Torsors, Étale Homotopy and Applications to Rational Points

Alexei N. Skorobogatov
Torsors tale Homotopy and Applications to Rational Points Book PDF

Author : Alexei N. Skorobogatov
Publisher : Cambridge University Press
Page : 470 pages
File Size : 54,5 Mb
Release : 2013-04-18
Category : Mathematics
ISBN : 9781107245266

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Torsors, Étale Homotopy and Applications to Rational Points by Alexei N. Skorobogatov Pdf

Torsors, also known as principal bundles or principal homogeneous spaces, are ubiquitous in mathematics. The purpose of this book is to present expository lecture notes and cutting-edge research papers on the theory and applications of torsors and étale homotopy, all written from different perspectives by leading experts. Part one of the book contains lecture notes on recent uses of torsors in geometric invariant theory and representation theory, plus an introduction to the étale homotopy theory of Artin and Mazur. Part two of the book features a milestone paper on the étale homotopy approach to the arithmetic of rational points. Furthermore, the reader will find a collection of research articles on algebraic groups and homogeneous spaces, rational and K3 surfaces, geometric invariant theory, rational points, descent and the Brauer–Manin obstruction. Together, these give a state-of-the-art view of a broad area at the crossroads of number theory and algebraic geometry.

Torsors, Étale Homotopy and Applications to Rational Points

Alexei Skorobogatov
Torsors tale Homotopy and Applications to Rational Points Book PDF

Author : Alexei Skorobogatov
Publisher : Unknown
Page : 128 pages
File Size : 45,5 Mb
Release : 2013
Category : Algebra
ISBN : 110724806X

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Torsors, Étale Homotopy and Applications to Rational Points by Alexei Skorobogatov Pdf

Lecture notes and research articles on the use of torsors and étale homotopy in algebraic and arithmetic geometry.

Torsors, Etale Homotopy and Applications to Rational Points

Alexei Skorobogatov
Torsors Etale Homotopy and Applications to Rational Points Book PDF

Author : Alexei Skorobogatov
Publisher : Unknown
Page : 471 pages
File Size : 43,8 Mb
Release : 2014-05-14
Category : MATHEMATICS
ISBN : 1107250552

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Torsors, Etale Homotopy and Applications to Rational Points by Alexei Skorobogatov Pdf

Lecture notes and research articles on the use of torsors and etale homotopy in algebraic and arithmetic geometry.

Torsors, Étale Homotopy and Applications to Rational Points

Alexei Skorobogatov
Torsors tale Homotopy and Applications to Rational Points Book PDF

Author : Alexei Skorobogatov
Publisher : Cambridge University Press
Page : 470 pages
File Size : 51,9 Mb
Release : 2013-04-18
Category : Mathematics
ISBN : 9781107616127

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Torsors, Étale Homotopy and Applications to Rational Points by Alexei Skorobogatov Pdf

Lecture notes and research articles on the use of torsors and étale homotopy in algebraic and arithmetic geometry.

Torsors and Rational Points

Alexei Skorobogatov
Torsors and Rational Points Book PDF

Author : Alexei Skorobogatov
Publisher : Cambridge University Press
Page : 197 pages
File Size : 49,8 Mb
Release : 2001-07-05
Category : Mathematics
ISBN : 9780521802376

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Torsors and Rational Points by Alexei Skorobogatov Pdf

This book, first published in 2001, is a complete and coherent exposition of the theory and applications of torsors to rational points.

Algebraic Geometry

Richard Thomas
Algebraic Geometry Book PDF

Author : Richard Thomas
Publisher : American Mathematical Soc.
Page : 635 pages
File Size : 44,7 Mb
Release : 2018-06-01
Category : Geometry, Algebraic
ISBN : 9781470435783

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Algebraic Geometry by Richard Thomas Pdf

This is Part 2 of a two-volume set. Since Oscar Zariski organized a meeting in 1954, there has been a major algebraic geometry meeting every decade: Woods Hole (1964), Arcata (1974), Bowdoin (1985), Santa Cruz (1995), and Seattle (2005). The American Mathematical Society has supported these summer institutes for over 50 years. Their proceedings volumes have been extremely influential, summarizing the state of algebraic geometry at the time and pointing to future developments. The most recent Summer Institute in Algebraic Geometry was held July 2015 at the University of Utah in Salt Lake City, sponsored by the AMS with the collaboration of the Clay Mathematics Institute. This volume includes surveys growing out of plenary lectures and seminar talks during the meeting. Some present a broad overview of their topics, while others develop a distinctive perspective on an emerging topic. Topics span both complex algebraic geometry and arithmetic questions, specifically, analytic techniques, enumerative geometry, moduli theory, derived categories, birational geometry, tropical geometry, Diophantine questions, geometric representation theory, characteristic and -adic tools, etc. The resulting articles will be important references in these areas for years to come.

Cox Rings

Ivan Arzhantsev
Cox Rings Book PDF

Author : Ivan Arzhantsev
Publisher : Cambridge University Press
Page : 539 pages
File Size : 42,8 Mb
Release : 2015
Category : Mathematics
ISBN : 9781107024625

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Cox Rings by Ivan Arzhantsev Pdf

This book provides a largely self-contained introduction to Cox rings and their applications in algebraic and arithmetic geometry.

The Brauer–Grothendieck Group

Jean-Louis Colliot-Thélène,Alexei N. Skorobogatov
The Brauer Grothendieck Group Book PDF

Author : Jean-Louis Colliot-Thélène,Alexei N. Skorobogatov
Publisher : Springer Nature
Page : 450 pages
File Size : 41,6 Mb
Release : 2021-07-30
Category : Mathematics
ISBN : 9783030742485

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The Brauer–Grothendieck Group by Jean-Louis Colliot-Thélène,Alexei N. Skorobogatov Pdf

This monograph provides a systematic treatment of the Brauer group of schemes, from the foundational work of Grothendieck to recent applications in arithmetic and algebraic geometry. The importance of the cohomological Brauer group for applications to Diophantine equations and algebraic geometry was discovered soon after this group was introduced by Grothendieck. The Brauer–Manin obstruction plays a crucial role in the study of rational points on varieties over global fields. The birational invariance of the Brauer group was recently used in a novel way to establish the irrationality of many new classes of algebraic varieties. The book covers the vast theory underpinning these and other applications. Intended as an introduction to cohomological methods in algebraic geometry, most of the book is accessible to readers with a knowledge of algebra, algebraic geometry and algebraic number theory at graduate level. Much of the more advanced material is not readily available in book form elsewhere; notably, de Jong’s proof of Gabber’s theorem, the specialisation method and applications of the Brauer group to rationality questions, an in-depth study of the Brauer–Manin obstruction, and proof of the finiteness theorem for the Brauer group of abelian varieties and K3 surfaces over finitely generated fields. The book surveys recent work but also gives detailed proofs of basic theorems, maintaining a balance between general theory and concrete examples. Over half a century after Grothendieck's foundational seminars on the topic, The Brauer–Grothendieck Group is a treatise that fills a longstanding gap in the literature, providing researchers, including research students, with a valuable reference on a central object of algebraic and arithmetic geometry.

Homotopy Theory and Arithmetic Geometry – Motivic and Diophantine Aspects

Frank Neumann,Ambrus Pál
Homotopy Theory and Arithmetic Geometry Motivic and Diophantine Aspects Book PDF

Author : Frank Neumann,Ambrus Pál
Publisher : Springer Nature
Page : 223 pages
File Size : 44,7 Mb
Release : 2021-09-29
Category : Mathematics
ISBN : 9783030789770

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Homotopy Theory and Arithmetic Geometry – Motivic and Diophantine Aspects by Frank Neumann,Ambrus Pál Pdf

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.

Torsors, Reductive Group Schemes and Extended Affine Lie Algebras

Philippe Gille,Arturo Pianzola
Torsors Reductive Group Schemes and Extended Affine Lie Algebras Book PDF

Author : Philippe Gille,Arturo Pianzola
Publisher : American Mathematical Soc.
Page : 112 pages
File Size : 53,5 Mb
Release : 2013-10-23
Category : Mathematics
ISBN : 9780821887745

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Torsors, Reductive Group Schemes and Extended Affine Lie Algebras by Philippe Gille,Arturo Pianzola Pdf

The authors give a detailed description of the torsors that correspond to multiloop algebras. These algebras are twisted forms of simple Lie algebras extended over Laurent polynomial rings. They play a crucial role in the construction of Extended Affine Lie Algebras (which are higher nullity analogues of the affine Kac-Moody Lie algebras). The torsor approach that the authors take draws heavily from the theory of reductive group schemes developed by M. Demazure and A. Grothendieck. It also allows the authors to find a bridge between multiloop algebras and the work of F. Bruhat and J. Tits on reductive groups over complete local fields.

Handbook of Homotopy Theory

Haynes Miller
Handbook of Homotopy Theory Book PDF

Author : Haynes Miller
Publisher : CRC Press
Page : 982 pages
File Size : 43,9 Mb
Release : 2020-01-23
Category : Mathematics
ISBN : 9781351251617

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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.

Rational Points on Varieties

Bjorn Poonen
Rational Points on Varieties Book PDF

Author : Bjorn Poonen
Publisher : Unknown
Page : 128 pages
File Size : 41,6 Mb
Release : 2017
Category : MATHEMATICS
ISBN : 1470443155

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Rational Points on Varieties by Bjorn Poonen Pdf

This book is motivated by the problem of determining the set of rational points on a variety, but its true goal is to equip readers with a broad range of tools essential for current research in algebraic geometry and number theory. The book is unconventional in that it provides concise accounts of many topics instead of a comprehensive account of just one-this is intentionally designed to bring readers up to speed rapidly. Among the topics included are Brauer groups, faithfully flat descent, algebraic groups, torsors, étale and fppf cohomology, the Weil conjectures, and the Brauer-Manin and de.

Advances in Two-Dimensional Homotopy and Combinatorial Group Theory

Wolfgang Metzler,Stephan Rosebrock
Advances in Two Dimensional Homotopy and Combinatorial Group Theory Book PDF

Author : Wolfgang Metzler,Stephan Rosebrock
Publisher : Cambridge University Press
Page : 193 pages
File Size : 44,8 Mb
Release : 2018
Category : Mathematics
ISBN : 9781316600900

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Advances in Two-Dimensional Homotopy and Combinatorial Group Theory by Wolfgang Metzler,Stephan Rosebrock Pdf

Presents the current state of knowledge in all aspects of two-dimensional homotopy theory. Useful for both students and experts.

Geometry Over Nonclosed Fields

Fedor Bogomolov,Brendan Hassett,Yuri Tschinkel
Geometry Over Nonclosed Fields Book PDF

Author : Fedor Bogomolov,Brendan Hassett,Yuri Tschinkel
Publisher : Springer
Page : 261 pages
File Size : 54,5 Mb
Release : 2017-02-09
Category : Mathematics
ISBN : 9783319497631

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Geometry Over Nonclosed Fields by Fedor Bogomolov,Brendan Hassett,Yuri Tschinkel Pdf

Based on the Simons Symposia held in 2015, the proceedings in this volume focus on rational curves on higher-dimensional algebraic varieties and applications of the theory of curves to arithmetic problems. There has been significant progress in this field with major new results, which have given new impetus to the study of rational curves and spaces of rational curves on K3 surfaces and their higher-dimensional generalizations. One main recent insight the book covers is the idea that the geometry of rational curves is tightly coupled to properties of derived categories of sheaves on K3 surfaces. The implementation of this idea led to proofs of long-standing conjectures concerning birational properties of holomorphic symplectic varieties, which in turn should yield new theorems in arithmetic. This proceedings volume covers these new insights in detail.

Algebraic Combinatorics and the Monster Group

Alexander A. Ivanov
Algebraic Combinatorics and the Monster Group Book PDF

Author : Alexander A. Ivanov
Publisher : Cambridge University Press
Page : 584 pages
File Size : 55,8 Mb
Release : 2023-08-17
Category : Mathematics
ISBN : 9781009338059

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Algebraic Combinatorics and the Monster Group by Alexander A. Ivanov Pdf

Covering, arguably, one of the most attractive and mysterious mathematical objects, the Monster group, this text strives to provide an insightful introduction and the discusses the current state of the field. The Monster group is related to many areas of mathematics, as well as physics, from number theory to string theory. This book cuts through the complex nature of the field, highlighting some of the mysteries and intricate relationships involved. Containing many meaningful examples and a manual introduction to the computer package GAP, it provides the opportunity and resources for readers to start their own calculations. Some 20 experts here share their expertise spanning this exciting field, and the resulting volume is ideal for researchers and graduate students working in Combinatorial Algebra, Group theory and related areas.