Bertini theorem for normality on local rings in mixed characteristic (applications to characteristic ideals)

TL;DR

This paper proves a strong local Bertini theorem for normality in mixed characteristic local rings, showing that generic hyperplane sections preserve normality in certain algebraic structures, with applications to characteristic ideals.

Contribution

It establishes a new strong version of the local Bertini theorem for normality in mixed characteristic, extending the understanding of hyperplane sections in algebraic geometry.

Findings

Normal hyperplane sections are normal in mixed characteristic settings.

Applications to characteristic ideals in torsion modules.

Supports advances in Euler system and Iwasawa theory.

Abstract

In this article, we prove a strong version of local Bertini theorem for normality on local rings in mixed characteristic. The main result asserts that a generic hyperplane section of a normal, Cohen-Macaulay, and complete local domain of dimension at least 3 is normal. Applications include the study of characteristic ideals attached to torsion modules over Noetherian normal domains, which is fundamental in the study of Euler system theory over normal domains and Iwasawa main conjectures.