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Speaker:
Masha Vlasenko
Affiliation:
University College Dublin
Date:
Wed, 14/01/2015 - 16:30 - 17:30
Location:
MPIM Lecture Hall
Parent event:
Seminar "Recurrences and L-values" We prove p-adic continuity of the matrices of coefficients of the logarithm of the Artin-Mazur formal group law associated to a projective hypersurface. The coefficient matrices were computed explicitly by Jan Stienstra in 1987, who also proved they satisfy congruences of Atkin and Swinnerton-Dyer type for a wide class of hypersurfaces, namely double covers of a projective space. In the case when reduction modulo p is a nonsingular hypersurface, Stienstra's congruences imply that eigenvalues of our limiting matrices are eigenvalues of Frobenius of zero p-adic valuation on the middle crystalline cohomology of the reduction of the hypersurface modulo p.
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