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

Part of: Differential algebra Local rings and semilocal rings

Published online by Cambridge University Press:  11 January 2016

Tadashi Ochiai  and
Kazuma Shimomoto
Tadashi Ochiai
Affiliation:
Graduate school of Science, Osaka University 1-1, Machikaneyama Toyonaka, Osaka 560-0043, Japan, [email protected]
Kazuma Shimomoto
Affiliation:
Department of Mathematics, School of Science and Technology, Meiji University 1-1-1, Higashimita Tama-Ku Kawasaki 214-8571, Japan, [email protected]
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Abstract

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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.

MSC classification

Secondary: 13H10: Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) 13N05: Modules of differentials
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 218 , June 2015 , pp. 125 - 173
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2015

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