The main conjecture of Iwasawa theory for totally real fields

DOI10.1007/s00222-012-0436-xzbMath1300.11112arXiv1008.0142OpenAlexW2050110171WikidataQ123107705 ScholiaQ123107705MaRDI QIDQ376217

Mahesh Kakde

Publication date: 4 November 2013

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1008.0142

zbMATH Keywords

\(L\)-functionsIwasawa theory\(K\)-theory\(p\)-adic Lie-groupsmain conjecture

Mathematics Subject Classification ID

Zeta functions and (L)-functions of number fields (11R42) Iwasawa theory (11R23) (K_1) of group rings and orders (19B28) Totally real fields (11R80)

Related Items (23)

$\mathfrak{M}_H(G)$-property and congruence of Galois representations ⋮ Integrality of Stickelberger elements and the equivariant Tamagawa number conjecture ⋮ On the cohomology of Kobayashi’s plus/minus norm groups and applications ⋮ \(SK_1\) and Lie algebras ⋮ On derivatives of \(p\)-adic \(L\)-series at \(s = 0\) ⋮ On free resolutions of Iwasawa modules ⋮ \({K}_{1}\)-congruences for three-dimensional Lie groups ⋮ When do reduced Whitehead groups of Iwasawa algebras vanish? A reduction step ⋮ On a noncommutative Iwasawa main conjecture for varieties over finite fields ⋮ Poitou-Tate duality over extensions of global fields ⋮ On Geometric Iwasawa Theory and Special Values of Zeta Functions ⋮ On the p‐adic Stark conjecture at s=1 and applications ⋮ Introduction to the Work of M. Kakde on the Non-commutative Main Conjectures for Totally Real Fields ⋮ The Group Logarithm Past and Present ⋮ \(\mathrm{K}_1\) of a \(p\)-adic group ring. II: The determinantal kernel \(\mathrm{SK}_1\) ⋮ HIGHER ORDER CONGRUENCES AMONGST HASSE–WEIL -VALUES ⋮ On the \(p\)-adic Beilinson conjecture and the equivariant Tamagawa number conjecture ⋮ On the non-abelian Brumer-Stark conjecture and the equivariant Iwasawa main conjecture ⋮ Non-commutative \(L\)-functions for \(p\)-adic representations over totally real fields ⋮ Conjectures of Brumer, Gross and Stark ⋮ On Equivariant Characteristic Ideals of Real Classes ⋮ Kato's local epsilon conjecture:l≠pcase ⋮ Some Congruences for Non-CM Elliptic Curves

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