Abstract
These notes are supposed to serve as a condensed but approachable guide to the way étale homotopy can be used to study rational points. I hope readers from different backgrounds will find it useful, but it is probably most suitable for a reader with some background in algebraic geometry who is not necessarily as familiar with modern homotopical and ∞-categorical methods. The original definition of the étale homotopy type is due to Artin and Mazur, and the idea was further developed by Friedlander. In recent years there has been a lot of activity around étale homotopy and its applications.
| Original language | American English |
|---|---|
| Title of host publication | Lecture Notes in Mathematics |
| Publisher | Springer Science and Business Media Deutschland GmbH |
| Pages | 107-143 |
| Number of pages | 37 |
| DOIs | |
| State | Published - 2021 |
Publication series
| Name | Lecture Notes in Mathematics |
|---|---|
| Volume | 2292 |
| ISSN (Print) | 0075-8434 |
| ISSN (Electronic) | 1617-9692 |
Bibliographical note
Funding Information:The text is based on the talks given by the author in the LMS Research School on “Homotopy Theory and Arithmetic Geometry: Motivic and Diophantine Aspects” held in imperial college in July 2018. I wish to thank Frank Neumann and Ambrus Pál for organising this outstanding event and inviting me to speak in it. I would like to thank Shay Ben Moshe for his remarks on the first draft. Finally, I would also like to thank Shachar Carmeli and Lior Yanovski for their indispensable help with the preparation of this notes.
Publisher Copyright:
© 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.