Seminar series
Date
Thu, 01 Nov 2018
Time
16:00 -
17:00
Location
L6
Speaker
Daniel Gulotta
Organisation
Oxford University
Let F be a totally real or CM number field. Scholze has constructed Galois representations associated with torsion classes in the cohomology of locally symmetric spaces for GL_n(F). We show that the nilpotent ideal appearing in Scholze's construction can be removed when F splits completely at the relevant prime. As a key component of the proof, we show that the compactly supported cohomology of certain unitary and symplectic Shimura varieties with level Gamma_1(p^{\infty}) vanishes above the middle degree. This is joint work with Ana Caraiani, Chi-Yun Hsu, Christian Johansson, Lucia Mocz, Emanuel Reinecke, and Sheng-Chi Shih.