Format:
1 Online-Ressource (IX, 218 p.)
ISBN:
9783030789770
Series Statement:
Lecture Notes in Mathematics 2292
Content:
- 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. Étale Homotopy and Obstructions to Rational Points -- 5. A1-Homotopy Theory and Contractible Varieties: a Survey -- Index.
Content:
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.
Additional Edition:
ISBN 9783030789763
Additional Edition:
ISBN 9783030789787
Additional Edition:
Erscheint auch als Druck-Ausgabe ISBN 9783030789787
Additional Edition:
Erscheint auch als Druck-Ausgabe Homotopy theory and arithmetic geometry – motivic and diophantine aspects Cham : Springer, 2021 ISBN 9783030789763
Language:
English
Keywords:
Algebraische Topologie
;
Arithmetische Geometrie
;
Konferenzschrift
DOI:
10.1007/978-3-030-78977-0
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