The Zeta-function of Monomial Deformations of Fermat Hypersurfaces
نویسنده
چکیده
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 [4], [9]. In doing so, we obtain concrete and explicit examples for some results recently used in algorithms to count points on smooth hypersurfaces in Pn. 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 (Theorem 3.10) we obtain Poincaré Duality for the Rigid cohomology of certain singular affine varieties.
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