The main conjecture of Iwasawa theory for totally real fields

Abstract

The purpose of this paper is to prove the main conjecture of noncommutative Iwasawa theory for p-adic Lie extensions for totally real fields, for an odd prime p, assuming Iwasawa's conjecture on vanishing of the cyclotomic µ-invariant for certain CM extension of the base field.

Iwasawa Theory 2012

“…After the recent proof of the non commutative EMC (under the hypothesis that D 0, see Kakde 2013;Ritter and Weiss 2011), no doubt that the above results could be extended to the case where G is non abelian (this has been done recently by Nickel 2013). But in this article, we are mainly interested in the odd twists, m Á 1 (mod 2), which are not a priori covered by the EMC.…”

Algebraische Zahlentheorie

“…One of the central difficulties of the theory seems to be the construction of non-abelian p-adic L-functions. Actually, the only known results in this direction are mainly restricted to the Tate motive thanks to the works of Ritter and Weiss in [14,15] and Kakde [13].…”

K1 of a p-adic group ring II. The determinantal kernel SK1

“…The present paper is the second in a series of two papers: the first paper [3] dealt with the determinantal image of K 1 (R[G]), whereas this paper is concerned with the kernel of the determinant map, SK 1 (R[G]). It is interesting to note that recently there has been considerable resurgence of interest in K 1 of group rings with higher dimensional rings of coefficients in equivariant Iwasawa theory (see for instance [8,13,[10][11][12]21,22]). …”