Introduction to the Work of M. Kakde on the Non-commutative Main Conjectures for Totally Real Fields

DOI10.1007/978-3-642-32199-3_1zbMath1270.11107OpenAlexW143575317MaRDI QIDQ4912832

John H. Coates, Do-Hyeong Kim

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://doi.org/10.1007/978-3-642-32199-3_1

zbMATH Keywords

main conjecturemotiveIwasawa algebras

Mathematics Subject Classification ID

Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.) (16E65) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Elliptic curves over global fields (11G05) Iwasawa theory (11R23) Filtered associative rings; filtrational and graded techniques (16W70)

Related Items (3)

Reductions of the Main Conjecture ⋮ Congruences Between Abelian p-Adic Zeta Functions ⋮ On p-Adic Artin L-Functions II

Cites Work

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• The main conjecture of Iwasawa theory for totally real fields
• On \(\mathbb Z_{\ell}\)-extensions of algebraic number fields
• On the structure theory of the Iwasawa algebra of a \(p\)-adic Lie group.
• Deforming Galois representations and the conjectures of Serre and Fontaine-Mazur.
• The \(\text{GL}_2\) main conjecture for elliptic curves without complex multiplication
• \(K_1\) of some non-commutative completed group rings
• The Iwasawa conjecture for totally real fields
• On the “main conjecture” of equivariant Iwasawa theory
• Onp-adic ArtinL-functions
• On the ranks of Iwasawa modules over $p$ -adic Lie extensions
• EULER CHARACTERISTICS AS INVARIANTS OF IWASAWA MODULES
• Cohomology of Group Extensions

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