Bertini theorem for normality on local rings in mixed characteristic (applications to characteristic ideals)
Number Theory
2015-06-18 v3 Commutative Algebra
Algebraic Geometry
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.
Keywords
Cite
@article{arxiv.1108.4708,
title = {Bertini theorem for normality on local rings in mixed characteristic (applications to characteristic ideals)},
author = {Tadashi Ochiai and Kazuma Shimomoto},
journal= {arXiv preprint arXiv:1108.4708},
year = {2015}
}
Comments
revised version, published in Nagoya Math. Jour