Étale Homotopy and Obstructions to Rational Points

Tomer M. Schlank*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


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 languageAmerican English
Title of host publicationLecture Notes in Mathematics
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages37
StatePublished - 2021

Publication series

NameLecture Notes in Mathematics
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.


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