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Homotopy theory and arithmetic geome...

Neumann, Frank.

Homotopy theory and arithmetic geometry - Motivic and Diophantine aspectsLMS-CMI Research School, London, July 2018 /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Homotopy theory and arithmetic geometry - Motivic and Diophantine aspectsedited by Frank Neumann, Ambrus Pal.
Reminder of title:	LMS-CMI Research School, London, July 2018 /
other author:	Neumann, Frank.
Published:	Cham :Springer International Publishing :2021.
Description:	ix, 218 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Homotopy theoryTextbooks.
Online resource:	https://doi.org/10.1007/978-3-030-78977-0
ISBN:	9783030789770$q(electronic bk.)

Homotopy theory and arithmetic geometry - Motivic and Diophantine aspectsLMS-CMI Research School, London, July 2018 /
Homotopy theory and arithmetic geometry - Motivic and Diophantine aspectsLMS-CMI Research School, London, July 2018 /[electronic resource] :edited by Frank Neumann, Ambrus Pal. - Cham :Springer International Publishing :2021. - ix, 218 p. :ill., digital ;24 cm. - Lecture notes in mathematics,v.22921617-9692 ;. - Lecture notes in mathematics ;2035..

1. Homotopy Theory and Arithmetic Geometry - Motivic and Diophantine Aspects: an Introduction -- 2. An Introduction to A1-Enumerative Geometry -- 3. Cohomological Methods in Intersection Theory -- 4. Etale Homotopy and Obstructions to Rational Points -- 5. A1-Homotopy Theory and Contractible Varieties: a Survey -- Index.

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 etale homotopy theory for obstructions to the existence of rational points on algebraic varieties. Finally, the article by Asok and Ostvaer, based in part on the Nelder Fellow lecture series by Ostvaer, 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.

ISBN: 9783030789770$q(electronic bk.)

Standard No.: 10.1007/978-3-030-78977-0doiSubjects--Topical Terms:

522739
Homotopy theory
--Textbooks.

LC Class. No.: QA612.7

Dewey Class. No.: 514.24

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520 $a 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 etale homotopy theory for obstructions to the existence of rational points on algebraic varieties. Finally, the article by Asok and Ostvaer, based in part on the Nelder Fellow lecture series by Ostvaer, 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.
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