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Bertini theorem for normality on local rings in mixed characteristic (applications to characteristic ideals). (English) Zbl 1325.13023

In this article, the authors 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”. Moreover, the paper contains some applications including 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:

13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)
13F35 Witt vectors and related rings
13N05 Modules of differentials
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