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HIOB 19/20: Étale Homotopy Type

The topic of this semester's HIOB (Higher Invariants Oberseminar) is the étale homotopy type of schemes.

The first few talks will be about the classical étale fundamental group of schemes its pro- étale cousin as developed by Bhatt and Scholze. These invariants can be seen as part of the homotopy type and already contain a lot (and sometimes even all) of the information. The second half is devoted to introducing the étale homotopy type of a scheme and finally prove the generalized Riemann existence theorem. For this we develop a very general form of Galois-Theory due to Lurie and Hoyois which might be of interest on its own.

This seminar is designed as a learning seminar for anyone interested. Prerequisites for the first half will only be very basic algebraic geometry. For the second half we chose a very modern approach which requires some fluency with infinity categories. Yet we hope that anyone who is willing to accept some blackboxes can follow the whole seminar. As we will see throughout the seminar, infinity-topoi are simply the most natural setting for defining and studying the étale homotopy type of schemes.

Dates and location

Mondays, 12-14, SFB Seminar Room.

Program

The detailed program can be found here(updated 13.10.).

Talks

If you are interested in giving a talk in this seminar, please contact Benedikt Preis.

Talk		Date	Title	Speaker
1	14.	October	Introduction and overview	Benedikt Preis
2	21.	October	Étale Fundamental Group I: Abstract Galois Theory	Marco Volpe
3	28.	October	Étale Fundamental Group II: Definition	Yassin Mousa
4	4.	November	Étale Fundamental Group III: Some key properties	Johannes Sprang
5	11.	November	The Pro-Étale Topology and infinite Galois Categories	Marta Barigozzi
6	18.	November	The Pro-Étale fundamental group	Han-Ung Kufner
7	25.	November	Pro-∞-categories and Shape	Benedikt Preis
8	2.	December	Shape and Torsors	Charanya Ravi
9	9.	December	no seminar due to windberg	no speaker
10	16.	December	Finite Galois Theory	Maria Yakerson
11	13.	January	Cohomology in ∞-topoi	Denis Nardin
12	20.	January	Infinite Galois Theory and the shape of nice topological spaces	Marco Volpe
13	27.	January	Discussion : Next semester's topic	Starts at 13:00
14	3.	February	Talk postponed:The Riemann Existence Theorem	Denis-Charles Cisinski