Control of the non-geometrically integral reductions

TL;DR

This paper establishes an upper bound on the product of norms of non-geometrically integral reductions of a geometrically integral projective scheme over any number field, using an adelic approach.

Contribution

It introduces a novel upper bound for these norms, applying adelic methods to the study of reductions over number fields.

Findings

Upper bound for product of norms of non-geometrically integral reductions

Application of adelic viewpoint to reduction problems

Generalization over arbitrary number fields

Abstract

In this paper, for a geometrically integral projective scheme, we will give an upper bound of the product of the norms of its non-geometrically integral reductions over an arbitrary number field. For this aim, we take the adelic viewpoint on this subject.