中科院数学与系统科学研究院
数学研究所
数论研讨班
报告人: Ana Caraiani(Imperial College)
题 目:On the vanishing of cohomology for certain Shimura varieties
时 间:2018.01.17(星期三),17:00-18:00
地 点:数学院南楼N913室
摘 要: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.