Birational smooth minimal models have equal Hodge numbers in all dimensions

Details Birational smooth minimal models have equal Hodge numbers in all dimensions Birational smooth minimal models have equal Hodge numbers in all dimensions

2002-09-20

arxiv.org/abs/math/0209269v2

Mathematics

Number Theory

14 pages, AMS LaTeX, remarks and references added, to appear in the Proceedings of Calabi-Yau Varieties and Mirror Symmetry

Scientific paper

This is a resume of the author's talk at the Worhshop on Arithmetic, Geometry and Physics around Calabi-Yau Varieties and Mirror Symmetry (July 23-29, 2001), the Fields Institute. The aim of this note is to prove that birational smooth minimal models over C have equal Hodge numbers in all dimensions by an arithmetic method. Our method is a refinement of the method of V. Batyrev and C.-L. Wang on Betti numbers who used p-adic integration and the Weil conjecture. Our ingredient is to use further arithmetic results such as the Chebotarev density theorem and p-adic Hodge theory.

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