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

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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 
@article{SM_2021_212_12_a4,
     author = {D. N. Tyurin},
     title = {Generalization of the {Artin-Hasse} logarithm for the {Milnor} $K$-groups of $\delta$-rings},
     journal = {Sbornik. Mathematics},
     pages = {1746--1764},
     publisher = {mathdoc},
     volume = {212},
     number = {12},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2021_212_12_a4/}
}
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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/