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Stringy Hodge numbers and p-adic Hodge theory

Published online by Cambridge University Press:  15 October 2004

Tetsushi Ito
Tetsushi Ito
Affiliation:
Department of Mathematics, Faculty of Science, Kyoto University, Kyoto 606-8502, Japantetsushi@math.kyoto-u.ac.jp
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Abstract

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The aim of this paper is to give an application of p-adic Hodge theory to stringy Hodge numbers introduced by V. Batyrev for a mathematical formulation of mirror symmetry. Since the stringy Hodge numbers of an algebraic variety are defined by choosing a resolution of singularities, the well-definedness is not clear from the definition. We give a proof of the well-definedness by using arithmetic techniques such as p-adic integration and p-adic Hodge theory. Note that another proof of the well-definedness was obtained by V. Batyrev himself by motivic integration.

Keywords

stringy Hodge numbersp-adic integrationGalois representationp-adic Hodge theory11R4211S80 (primary)14E05 (secondary)
Type
Research Article
Information
Compositio Mathematica , Volume 140 , Issue 6 , November 2004 , pp. 1499 - 1517
Copyright
Foundation Compositio Mathematica 2004