Higher coherent cohomology in weight one

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Si-Ying Lee, Stanford University
IAS - Simonyi Hall 101

I will talk about a proof of local-global compatibility at p for higher coherent cohomology mod p in weight one for Hilbert modular varieties at an unramified prime, assuming we not in middle degree. I will discuss some key ingredients to the proof, including a geometric Jacquet-Langlands transfer map to suitable quaternionic Shimura varieties, and a doubling map in this setting.