Homotopy theory and arithmetic geometry – motivic and diophantine aspects: LMS-CMI Research School, London, July 2018
- 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 Varie...
Gespeichert in:
| Weitere Verfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cham
Springer
[2021]
|
| Schriftenreihe: | Lecture notes in mathematics
Volume 2292 |
| Schlagworte: | |
| Zusammenfassung: | - 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 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 |
| Beschreibung: | ix, 215 Seiten Diagramme |
| ISBN: | 9783030789763 |
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| 520 | 3 | |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 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 | |
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| spelling | Homotopy theory and arithmetic geometry – motivic and diophantine aspects LMS-CMI Research School, London, July 2018 Frank Neumann, Ambrus Pál, Editors Cham Springer [2021] ix, 215 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics Volume 2292 - 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 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 Algebraische Topologie (DE-588)4120861-4 gnd rswk-swf Arithmetische Geometrie (DE-588)4131383-5 gnd rswk-swf (DE-588)1071861417 Konferenzschrift gnd-content Algebraische Topologie (DE-588)4120861-4 s Arithmetische Geometrie (DE-588)4131383-5 s DE-604 Neumann, Frank (DE-588)1014996538 edt Ambrus, Pál (DE-588)124418487X edt Clay Mathematics Institute (DE-588)10038010-4 orm London Mathematical Society (DE-588)1011030-6 orm Erscheint auch als Online-Ausgabe 978-3-030-78977-0 (DE-604)BV047552451 Lecture notes in mathematics Volume 2292 (DE-604)BV000676446 2292 |
| spellingShingle | Homotopy theory and arithmetic geometry – motivic and diophantine aspects LMS-CMI Research School, London, July 2018 Lecture notes in mathematics Algebraische Topologie (DE-588)4120861-4 gnd Arithmetische Geometrie (DE-588)4131383-5 gnd |
| subject_GND | (DE-588)4120861-4 (DE-588)4131383-5 (DE-588)1071861417 |
| title | Homotopy theory and arithmetic geometry – motivic and diophantine aspects LMS-CMI Research School, London, July 2018 |
| title_auth | Homotopy theory and arithmetic geometry – motivic and diophantine aspects LMS-CMI Research School, London, July 2018 |
| title_exact_search | Homotopy theory and arithmetic geometry – motivic and diophantine aspects LMS-CMI Research School, London, July 2018 |
| title_exact_search_txtP | Homotopy theory and arithmetic geometry – motivic and diophantine aspects LMS-CMI Research School, London, July 2018 |
| title_full | Homotopy theory and arithmetic geometry – motivic and diophantine aspects LMS-CMI Research School, London, July 2018 Frank Neumann, Ambrus Pál, Editors |
| title_fullStr | Homotopy theory and arithmetic geometry – motivic and diophantine aspects LMS-CMI Research School, London, July 2018 Frank Neumann, Ambrus Pál, Editors |
| title_full_unstemmed | Homotopy theory and arithmetic geometry – motivic and diophantine aspects LMS-CMI Research School, London, July 2018 Frank Neumann, Ambrus Pál, Editors |
| title_short | Homotopy theory and arithmetic geometry – motivic and diophantine aspects |
| title_sort | homotopy theory and arithmetic geometry motivic and diophantine aspects lms cmi research school london july 2018 |
| title_sub | LMS-CMI Research School, London, July 2018 |
| topic | Algebraische Topologie (DE-588)4120861-4 gnd Arithmetische Geometrie (DE-588)4131383-5 gnd |
| topic_facet | Algebraische Topologie Arithmetische Geometrie Konferenzschrift |
| volume_link | (DE-604)BV000676446 |
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