The zeta-function of monomial deformations of Fermat hypersurfaces

Details The zeta-function of monomial deformations of Fermat hypersurfaces The zeta-function of monomial deformations of Fermat hypersurfaces

2007-03-05

arxiv.org/abs/math/0703120v2

Mathematics

Number Theory

Some proofs expanded, correction of some minor errors

Scientific paper

This paper intends to give a mathematical explanation for results on the zeta-function of some families of varieties recently obtained in the context of Mirror Symmetry. In doing so, we obtain concrete and explicit examples for some results recently used in algorithms to count points on smooth hypersurfaces in P^n. In particular, we extend the monomial-motive correspondence of Kadir and Yui and we give explicit solutions to the p-adic Picard-Fuchs equation associated with monomial deformations of Fermat hypersurfaces. As a by-product we obtain Poincare Duality for the Rigid cohomology of certain singular affine varieties.

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