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Berkeley-Caltech-Stanford Joint Number Theory Seminar

Monday, February 28, 2022
12:30pm to 1:30pm
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Online Event
Moduli of Fontaine-Laffaille modules and mod p local-global compatibility
Bao Le Hung, Department of Mathematics, Northwestern University,

The mod p cohomology of locally symmetric spaces for definite unitary groups at infinite level is expected to realize the mod p local Langlands correspondence for GL_n. In particular, one expects the (component at p) of the associated Galois representation to be determined by cohomology as a smooth representation. I will describe how one can establish this expectation in almost all cases when the local Galois representation is in the Fontaine-Laffaille range.
The main tool is a geometric study of the moduli space of Fontaine-Laffaille modules and the construction of enough functions on it through automorphic means.

This is joint work with D. Le, S. Morra, C. Park and Z. Qian.

For more information, please contact Math Department by phone at 626-395-4335 or by email at [email protected].