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June 2015 Bertini theorem for normality on local rings in mixed characteristic (applications to characteristic ideals)
Tadashi Ochiai, Kazuma Shimomoto
Nagoya Math. J. 218: 125-173 (June 2015). DOI: 10.1215/00277630-2891620

Abstract

In this article, we prove a strong version of the 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 normal domains, which is fundamental in the study of Euler system theory, Iwasawa’s main conjectures, and the deformation theory of Galois representations.

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Tadashi Ochiai. Kazuma Shimomoto. "Bertini theorem for normality on local rings in mixed characteristic (applications to characteristic ideals)." Nagoya Math. J. 218 125 - 173, June 2015. https://doi.org/10.1215/00277630-2891620

Information

Published: June 2015
First available in Project Euclid: 11 May 2015

zbMATH: 1325.13023
MathSciNet: MR3345626
Digital Object Identifier: 10.1215/00277630-2891620

Subjects:
Primary: 13H10
Secondary: 13K05 , 13N05

Keywords: Bertini-type theorem , characteristic ideal , differential module , hyperplane section

Rights: Copyright © 2015 Editorial Board, Nagoya Mathematical Journal

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Vol.218 • June 2015
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