K 1 of Certain Iwasawa Algebras, After Kakde

DOI10.1007/978-3-642-32199-3_4zbMath1270.11110arXiv1110.6362OpenAlexW1580116795MaRDI QIDQ4912835

Otmar Venjakob, Peter Schneider

Publication date: 26 March 2013

Published in: Noncommutative Iwasawa Main Conjectures over Totally Real Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.6362

zbMATH Keywords

completed group ringIwasawa algebraskew Laurent seriesalgebraic K-groupintegral group logarithm

Mathematics Subject Classification ID

Valuations, completions, formal power series and related constructions (associative rings and algebras) (16W60) Integral representations (11S23) Iwasawa theory (11R23) (K_1) of group rings and orders (19B28)

Related Items (3)

Reductions of the Main Conjecture ⋮ Congruences Between Abelian p-Adic Zeta Functions ⋮ On the Work of Ritter and Weiss in Comparison with Kakde’s Approach

Cites Work

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• A splitting for \(K_{1}\) of completed group rings
• A logarithmic approach to classgroups of integral group rings
• The \(\text{GL}_2\) main conjecture for elliptic curves without complex multiplication
• Proof of the main conjecture of noncommutative Iwasawa theory for totally real number fields in certain cases
• Localizations and completions of skew power series rings
• Logarithmic descriptions of Whitehead groups and class groups for 𝑝-groups
• The Group Logarithm Past and Present
• Endliche Gruppen I

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