Cohomology of Siegel Varieties with p-adic integral coefficients and Applications

Details Cohomology of Siegel Varieties with p-adic integral coefficients and Applications Cohomology of Siegel Varieties with p-adic integral coefficients and Applications

2000-12-12

arxiv.org/abs/math/0012090v1

Mathematics

Algebraic Geometry

116 pages, updated version of preprint of University Paris-Nord 2000-03

Scientific paper

Under the assumption that Galois representations associated to Siegel modular forms exist (it is known only for genus at most 2), we show that the cohomology with p-adic integral coefficients of Siegel Varieties, when localized at a non-Eisenstein maximal ideal of the Hecke algebra, is torsion-free, provided the prime p is large with the respect to the weight of the coefficient system. The proof uses p-adic Hodge theory, the dual BGG complex modulo p in order to compute the Hodge-Tate weights for the mod p cohomology. We apply this result to the construction of Hida p-adic families for symplectic groups and to the first step in the construction of a Taylor-Wiles system for these groups.

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