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SUMMARY:On the vanishing of cohomology for certain Shimura varieties
DTSTART;VALUE=DATE-TIME:20180117T090000Z
DTEND;VALUE=DATE-TIME:20180117T100000Z
DTSTAMP;VALUE=DATE-TIME:20210623T121150Z
UID:indico-event-3095@indico.math.cnrs.fr
DESCRIPTION:I will prove that the compactly supported cohomology of certai
n unitary or symplectic Shimura varieties at level Gamma_1(p^\\infty) vani
shes above the middle degree. The key ingredients come from p-adic Hodge t
heory 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 mod
el. I will also mention an application to Galois representations for torsi
on classes in the cohomology of locally symmetric spaces for GL_n. This ta
lk is based on joint work in preparation with D. Gulotta\, C.Y. Hsu\, C. J
ohansson\, L. Mocz\, E. Reineke\, and S.C. Shih.\n\nhttps://indico.math.cn
rs.fr/event/3095/
LOCATION:IHES Centre de confĂ©rences Marilyn et James Simons
URL:https://indico.math.cnrs.fr/event/3095/
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