## Journal of Differential Geometry

- J. Differential Geom.
- Volume 60, Number 2 (2002), 345-354.

### Cohomology Theory in Birational Geometry

#### Abstract

This is a continuation of [9], where it was shown that *K*-equivalent complex
projective manifolds have the same Betti numbers by using the theory of *p*-adic
integrals and Deligne's solution to the Weil conjecture. The aim of this note is to show
that with a little more book-keeping work, namely by applying Faltings' *p*-adic
Hodge Theory, our *p*-adic method also leads to the equivalence of Hodge numbers — a
result which was previously known via motivic integration.

#### Article information

**Source**

J. Differential Geom., Volume 60, Number 2 (2002), 345-354.

**Dates**

First available in Project Euclid: 20 July 2004

**Permanent link to this document**

https://projecteuclid.org/euclid.jdg/1090351105

**Digital Object Identifier**

doi:10.4310/jdg/1090351105

**Mathematical Reviews number (MathSciNet)**

MR1938116

**Zentralblatt MATH identifier**

1052.14016

#### Citation

Wang, Chin-Lung. Cohomology Theory in Birational Geometry. J. Differential Geom. 60 (2002), no. 2, 345--354. doi:10.4310/jdg/1090351105. https://projecteuclid.org/euclid.jdg/1090351105