Lecture----数学院晨兴数学中心

Title:	On the vanishing of cohomology for certain Shimura varieties
Speaker:	Ana Caraiani (Imperial College)
Time:	2018-1-17, 17:00-18:00
Place:	N913
Abstract:	I will prove that the compactly supported cohomology of certain unitary or symplectic Shimura varieties at level Gamma_1(p^\infty) vanishes above the middle degree. The key ingredients come from p-adic Hodge theory and studying the Bruhat decomposition on the Hodge-Tate flag variety. I will describe the steps in the proof using modular curves as a toy model. I will also mention an application to Galois representations for torsion classes in the cohomology of locally symmetric spaces for GL_n. This talk is based on joint work in preparation with D. Gulotta, C.Y. Hsu, C. Johansson, L. Mocz, E. Reineke, and S.C. Shih.
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