Jul 11 – 29, 2022
IHES
Europe/Paris timezone

Shimura Varieties and Modularity (3/3)

Jul 27, 2022, 9:20 AM
1h 20m
Marilyn and James Simons Conference Center (IHES)

Marilyn and James Simons Conference Center

IHES

35 route de Chartres, F-91440 Bures-sur-Yvette, France

Speakers

Prof. Ana CARAIANI (Imperial College) Prof. Sug Woo SHIN (UC Berkeley)

Description

We discuss vanishing theorems for the cohomology of Shimura varieties with torsion coefficients, under a genericity condition at an auxiliary prime. We describe two complementary approaches to these results, due to Caraiani-Scholze and Koshikawa, both of which rely on the geometry of the Hodge-Tate period morphism for the corresponding Shimura varieties. Finally, we explain how these vanishing results can be applied to local-global compatibility questions for the Galois representations constructed in the first lecture.

Presentation materials