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On the cohomology of locally symmetric spaces

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Ana Caraiani
Imperial College, London
Fri, 23/11/2018 - 15:30 - 16:30
MPIM Lecture Hall

I will discuss joint work in progress with Allen, Calegari, Gee, Helm, Le Hung, Newton, Scholze, Taylor, and Thorne on potential automorphy over CM fields. I will give an overview of this work and mention some applications. I will then focus on how to prove one of our key inputs, namely local-global compatibility at $l=p$ for certain Galois representations attached to torsion classes in the cohomology of locally symmetric spaces. This relies crucially on some ingredients from representation theory in positive characteristic.

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