Birational Calabi--Yau n-folds have equal Betti numbers

TL;DR

This paper proves that birational smooth projective Calabi--Yau n-folds over the complex numbers have identical Betti numbers, using p-adic analysis methods on algebraic varieties over local number fields.

Contribution

It introduces a novel approach employing p-adic analysis to establish Betti number invariance for birational Calabi--Yau varieties.

Findings

Birational Calabi--Yau n-folds have equal Betti numbers.

p-adic analysis is effective in studying algebraic varieties over local fields.

The result applies to smooth projective varieties with trivial canonical bundles.

Abstract

Let X and Y be two smooth projective n-dimensional algebraic varieties X and Y over C with trivial canonical line bundles. We use methods of p-adic analysis on algebraic varieties over local number fields to prove that if X and Y are birational, they have the same Betti numbers.