Betti number estimates in p-adic cohomology

TL;DR

This paper establishes p-adic Betti number estimates within Berthelot's arithmetic D-module framework and demonstrates their applications, advancing the understanding of p-adic cohomology in algebraic geometry.

Contribution

It provides the first p-adic analogue of Betti number estimates using Berthelot's theory, offering new tools for arithmetic geometry research.

Findings

Proved p-adic Betti number estimates

Applied estimates to specific arithmetic problems

Enhanced understanding of p-adic cohomology

Abstract

Within the framework of Berthelot's theory of arithmetic D-modules, we prove the p-adic analogue of Betti number estimates and we give some standard applications.