padic cohomology and classicality of overconvergent Hilbert modular forms
Yi Shao Tian (Paris/Beijing)
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When 
Nov 15, 2012 from 03:15 pm to 04:15 pm 
Where  Mainz, 05432 (Hilbertraum) 
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Abstract: Coleman showed in 1996 by a cohomological method that an overconvergent modular form of small slope is classical. In this talk, I will explain how to generalize Coleman's cohomological approach to overconvergent Hilbert cusp forms. Let F be a totally real field of degree $g>1$ in which p is unramified. Consider the GorenOort stratification of the special fiber of the Hilbert modular variety with hyperspecial level at p. We show first that each such stratum is a certain (P^1)^rbundle over (the special fiber) of another quaternionic Shimura variety. Using this geometric result, we show that the rigid cohomology of the ordinary locus of the Hilbert modular variety has the same Hecke spectrum as the space of classical cusp forms of Iwahori level at p. Then we deduce that a padic overconvergent Hilbert cuspidal eigenform of small slope is classical. We point out that the slope condition for classicality we obtained is better than that obtained by PilloniStroh, and was previously conjectured by Breuil.This is a joint work with Liang Xiao.