Stringy Hodge numbers and p-adic Hodge theory

Abstract

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.