Pseudonorms and p-adic birational Torelli theorem

TL;DR

This paper develops a p-adic analogue of a birational Torelli theorem using pseudonorms and image closure comparisons, providing new criteria for rational points on certain algebraic surfaces over finite fields.

Contribution

It introduces a p-adic pseudonorm framework for the birational Torelli theorem and establishes criteria for rational points on canonically polarized surfaces over finite fields.

Findings

Established a p-adic birational Torelli theorem analogue.

Provided a criterion for the existence of rational points on surfaces.

Connected pseudonorms with algebraic geometry over finite fields.

Abstract

A p-adic analogue of the pseudonorm version of the birational Torelli type theorem is obtained via a comparison theorem of image closures. Among other results obtained, we have a criterion for existence of rational points of canonically polarized surfaces over finite fields.