Cohomology of Siegel Varieties with padic integral coefficients and Applications
Abstract
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 padic integral coefficients of Siegel Varieties, when localized at a nonEisenstein maximal ideal of the Hecke algebra, is torsionfree, provided the prime p is large with the respect to the weight of the coefficient system. The proof uses padic Hodge theory, the dual BGG complex modulo p in order to compute the HodgeTate weights for the mod p cohomology. We apply this result to the construction of Hida padic families for symplectic groups and to the first step in the construction of a TaylorWiles system for these groups.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 December 2000
 arXiv:
 arXiv:math/0012090
 Bibcode:
 2000math.....12090M
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Number Theory;
 11F46;
 11G15;
 14K22;
 14F30
 EPrint:
 116 pages, updated version of preprint of University ParisNord 200003