Seminar on perfectoid Shimura varieties

organizer: Przemyslaw Chojecki

Date: September 2013 - December 2013; each Monday at 16h00 one talk 90-120 minutes.

Place: 4, place Jussieu (Paris, France); room 417, corridor 15-16 (4th floor)

Description of the seminar:

We will discuss the recent work of Peter Scholze [Sch1]. The main result we cover is the construction of Galois representations associated to regular algebraic automorphic representations. This is done by working with Siegel Shimura varieties at infinite level, which are perfectoid spaces, and constructing the Hodge-Tate period map. The period map is then used to p-adically approximate Hecke eigenvalues appearing in the completed cohomology of Siegel Shimura varieties. One concludes using different devissage techniques.

If time permits, we might also look into [HLTT], the work in which the construction of Galois representations for regular algebraic automorphic representations was done for the first time.

References:

[HLTT] M. Harris, K.W. Lan, R. Taylor, J. Thorne, "On the rigid cohomology of certain Shimura varieties"

[Sch1] P. Scholze, "On torsion in the cohomology of locally symmetric spaces"

[Sch2] P. Scholze, "Perfectoid spaces"

Timetable:

09.09.2013

Talk (Przemyslaw Chojecki): Adic spaces and basic notions of almost mathematics

16.09.2013

Talk (Riccardo Brasca): Perfectoid spaces

23.09.2013

Talk (Eugen Hellmann): Closed embeddings of perfectoid spaces and Hebbarkeitssatz (after Chapter II of [Sch1])

30.09.2013

Talk (Arthur-Cesar Le Bras): Siegel Shimura varieties and canonical subgroups (III.1 and III.2.1)

07.10.2013

Talk (Stephane Bijakowski): Canonical Frobenius lifts (III.2.2 and III.2.3)

14.10.2013

Talk (Przemyslaw Chojecki): Tate's traces and a strict neighbourhood of the anticanonical tower (III.2.4 and III.2.5)

21.10.2013

Talk (Riccardo Brasca): The Hodge-Tate period map (III.3)

28.10.2013

All-Saints' week (no seminar)

04.11.2013

Talk (David Hansen): Perfectoid Shimura varieties of Hodge type and completed cohomology (IV.1 and IV.2)

11.11.2013

Armistice (no seminar)

18.11.2013

We start at 16h30 because of the London-Paris number theory seminar before

Talk (Jean-Francois Dat): p-adic approximation on Hecke algebras (IV.3)

25.11.2013

Talk (Francesco Lemma): Cohomology of the boundary (V.1 and V.2)

02.12.2013

Talk (Giovanni Rosso): Determinants (V.3)

09.12.2013

Talk (Arthur-Cesar Le Bras): Conclusions: Galois representations associated to automorphic representations (V.4)