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 based on arithmetic results such as p-adic integration and p-adic Hodge theory. Note that another proof of the well-definedness was already obtained by V. Batyrev himself by motivic integration. This is a generalization of the author's earlier work in math.NT/0209269, where he treats only the smooth case.