Homotopy theory and arithmetic geometry : motivic and diophantine aspects : LMS-CMI Research School, London, July 2018
Author(s)
Bibliographic Information
Homotopy theory and arithmetic geometry : motivic and diophantine aspects : LMS-CMI Research School, London, July 2018
（Lecture notes in mathematics, 2292）
Springer, c2021
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
L/N||LNM||2292200043161071
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Includes bibliographical references and index
Description and Table of Contents
Description
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.
Table of Contents
- 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.
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