Generalization of the Artin-Hasse logarithm for the Milnor -groups of -rings

Let be a -adically complete ring equipped with a -structure. We construct a functorial group homomorphism from the Milnor -group to the quotient of the -adic completion of the module of differential forms . This homomorphism is a -adic analogue of the Bloch map defined for the relative Milnor -group...

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Bibliographic Details
Published in:Sbornik. Mathematics 2021-12, Vol.212 (12), p.1746-1764
Main Author: Tyurin, D. N.
Format: Article
Language:English
Subjects:
delta$-structures
differential forms
Frobenius lifting
Homomorphisms
Milnor $K$-groups
Citations: Items that this one cites
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Summary:Let be a -adically complete ring equipped with a -structure. We construct a functorial group homomorphism from the Milnor -group to the quotient of the -adic completion of the module of differential forms . This homomorphism is a -adic analogue of the Bloch map defined for the relative Milnor -groups of nilpotent extensions of rings of nilpotency degree for which the number is invertible. Bibliography: 12 titles.
ISSN:1064-5616
1468-4802
DOI:10.1070/SM9520