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.
De Pierre-Henri Chaudouard
De Pierre-Henri Chaudouard
De Lucas Mason-Brown
De Xinwen Zhu
De Xinwen Zhu
De Xinwen Zhu
De Tasho Kaletha
De Bao Chau Ngo
De Bao Chau Ngo
De Tasho Kaletha
De Matthew Emerton , Toby Gee , Eugen Hellmann
De Bao Chau Ngo
De Sam Raskin
De Sam Raskin
De Peter Scholze , Laurent Fargues
De Matthew Emerton , Toby Gee , Eugen Hellmann
De Matthew Emerton , Toby Gee , Eugen Hellmann
De Jean-François Dat
De Jessica Fintzen
De Peter Scholze , Laurent Fargues
De Matthew Emerton , Toby Gee , Eugen Hellmann
De Jessica Fintzen
De Jean-François Dat
De Peter Scholze , Laurent Fargues
De David Ben-Zvi
De Michael Harris , Tony Feng
De Yiannis Sakellaridis
De Michael Harris , Tony Feng
De Yiannis Sakellaridis
De Michael Harris , Tony Feng
De Alain Connes
De Teresa Krick
De Teresa Krick
![[1237] Moments de fonctions et $L$ stabilité homologique](/media/cache/video_light/uploads/video/Bourbaki.png)
