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

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

2011-08-23

arxiv.org/abs/1108.4708v1

Mathematics

Number Theory

Scientific paper

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.

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