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Sur la factorisation des fonctions zêta des hypersurfaces de Dwork

Abstract : This thesis deals with the factorisation of the zeta functions of the Dwork hypersurfaces. Candelas, de la Ossa and Rodriguez-Villegas found, in the case of the quintic, a factor coming from mirror symmetry and two factors coming from hypergeometric curves. Wan established the link with mirror symmetry in the general case, but the remaining factors have not been studied with the same level of detail as for the quintic, and it is on them that this thesis focuses. After a first chapter recalling the properties of the Dwork hypersurfaces, we establish, in chapter 2, an explicit factorisation of the zeta functions in terms of factors coming from hypersurfaces of hypergeometric type. In chapter 3, we deduce a factorisation of the zeta function from the isotypic decomposition of the cohomology of the Dwork hypersurfaces. Finally, in chapter 4, we link the two preceding factorisations.
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Contributor : Philippe Goutet <>
Submitted on : Thursday, December 10, 2009 - 3:03:47 PM
Last modification on : Thursday, December 10, 2020 - 10:51:54 AM
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  • HAL Id : tel-00440384, version 1


Philippe Goutet. Sur la factorisation des fonctions zêta des hypersurfaces de Dwork. Mathématiques [math]. Université Pierre et Marie Curie - Paris VI, 2009. Français. ⟨tel-00440384⟩



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