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Interpolating Periods

New Geometric Techniques in Number Theory July 01, 2013 - July 12, 2013

July 11, 2013 (02:45 PM PDT - 03:15 PM PDT)
Speaker(s): Shrenik Shah (Institute for Defense Analyses (CCR-LJ))
Location: SLMath: Eisenbud Auditorium
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Abstract We study the interpolation of Hodge-Tate and de Rham periods in families of Galois representations. Given a Galois representation on a coherent locally free sheaf over a reduced rigid space and a bounded range of weights, we obtain a stratification of this space by locally closed subvarieties where the Hodge-Tate and bounded de Rham periods (within this range) form locally free sheaves. At every thickened geometric point within one of the strata, we obtain a corresponding number of unbounded de Rham periods. If the number of interpolated de Rham periods is the number of fixed Hodge-Tate-Sen weights, we prove similar statements for non-reduced affinoid spaces. We also prove strong vanishing results for higher cohomology. These results encapsulate a robust theory of interpolation for Hodge-Tate and de Rham periods that simultaneously generalizes results of Berger-Colmez and Kisin.
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