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2007 The zeta function of monomial deformations of Fermat hypersurfaces
Remke Kloosterman
Algebra Number Theory 1(4): 421-450 (2007). DOI: 10.2140/ant.2007.1.421


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 the process we obtain concrete and explicit examples for some results recently used in algorithms to count points on smooth hypersurfaces in 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 byproduct we obtain Poincaré duality for the rigid cohomology of certain singular affine varieties.


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Remke Kloosterman. "The zeta function of monomial deformations of Fermat hypersurfaces." Algebra Number Theory 1 (4) 421 - 450, 2007.


Received: 5 March 2007; Revised: 31 August 2007; Accepted: 8 October 2007; Published: 2007
First available in Project Euclid: 20 December 2017

zbMATH: 1166.14016
MathSciNet: MR2368956
Digital Object Identifier: 10.2140/ant.2007.1.421

Primary: 14G10
Secondary: 11G25 , 14G15

Keywords: $p$-adic Picard–Fuchs equation , Monsky–Washnitzer cohomology , zeta function

Rights: Copyright © 2007 Mathematical Sciences Publishers


Vol.1 • No. 4 • 2007
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