K-группы Милнора и дифференциальные формы Тюрин Димитрий Николаевич

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Тюрин, Димитрий Николаевич.K-группы Милнора и дифференциальные формы = Milnor K-groups and differential forms : Milnor K-groups and differential forms : диссертация ... кандидата физико-математических наук : 01.01.06 / Tyurin Dimitry Nikolaevich; [Место защиты: ФГАОУ ВО «Национальный исследовательский университет «Высшая школа экономики»]. - Москва, 2021. - 80 с.

Оглавление диссертациикандидат наук Тюрин Димитрий Николаевич
Contents
Introduction
1 Preliminaries and supplementary results
1.1 Milnor K-groups
1.2 Weak k-stability
1.3 Differential forms
1.4 The map d log
1.5 i-rings
1.6 Differential forms of i-ring
1.7 Construction with filtered dg-rings
1.8 Derived p-adic completion
2 Milnor K-group of the ring of formal power series
2.1 Filtrations on the Milnor K-group
2.2 Construction of symbols from differential forms
2.3 Key result
2.4 Proof of Proposition
3 Bloch map
3.1 Bloch map for a split nilpotent extension
3.2 Category of split nilpotent extensions
3.3 Vanishing of relative de Rham cohomology
3.4 Finitely freely approximable functors
3.5 Construction of the Bloch map
4 Isomorphism theorem for the Bloch map
4.1 Reduction lemma
4.2 Special case of the isomorphism theorem
4.3 Proof of the isomorphism theorem
4.4 Non-existence of the Bloch map in a non-split case
5 Bloch—Artin—Hasse map
5.1 Artin-Hasse logarithm for i-rings
5.2 Bloch-Artin-Hasse map
5.3 Proof of Theorem
6 Isomorphism theorem for the Bloch—Artin—Hasse map
6.1 Isomorphism property for the Artin-Hasse logarithm
6.2 Isomorphism property for the Bloch-Artin-Hasse map
6.3 Proof of Theorem
7 Conclusion
8 References