Geodesic
Generalization of the Artin-Hasse logarithm for the Milnor $K$-groups of $\delta$-rings
Sbornik. Mathematics, Tome 212 (2021) no. 12, pp. 1746-1764 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $R$ be a $p$-adically complete ring equipped with a $\delta$-structure. We construct a functorial group homomorphism from the Milnor $K$-group $K^{M}_{n}(R)$ to the quotient of the $p$-adic completion of the module of differential forms $\widehat{\Omega}^{n-1}_{R}/d\widehat{\Omega}^{n-2}_{R}$. This homomorphism is a $p$-adic analogue of the Bloch map defined for the relative Milnor $K$-groups of nilpotent extensions of rings of nilpotency degree $N$ for which the number $N!$ is invertible. Bibliography: 12 titles.
Keywords: Milnor $K$-groups, differential forms, Frobenius lifting.
Mots-clés : $\delta$-structures 
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D. N. Tyurin. Generalization of the Artin-Hasse logarithm for the Milnor $K$-groups of $\delta$-rings. Sbornik. Mathematics, Tome 212 (2021) no. 12, pp. 1746-1764. http://geodesic.mathdoc.fr/item/SM_2021_212_12_a4/

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