Tadashi Ochiai

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

    Authors: Tadashi Ochiai, Kazuma Shimomoto
    Subjects: Number 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.

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