Holmstrom Iwasawa theory [private]

See my pile of printed notes and articles.

http://mathoverflow.net/questions/117394/applications-of-iwasawa-theory

http://mathoverflow.net/questions/108492/request-katos-article-lectures-on-the-approach-to-iwasawa-theory-for-hasse-wei

Collected papers of Iwasawa exist. Two volumes, ed Kato et al.

Greenberg: Iwasawa theory and p-adic deformation of motives (in Motives vol 2)

http://mathoverflow.net/questions/37374/what-is-a-path-in-k-theory-space

Note that I don’t have the Fukaya-Kato paper

Other authors studying Iwasawa theory include Greither, Popescu, Burns, Andreas Nickel, Henri Darmon.

[arXiv:1111.1645] Noncommutative Main Conjectures of Geometric Iwasawa Theory fra arXiv Front: math.NT av Malte Witte We give a survey on noncommutative main conjectures of Iwasawa theory in a geometric setting, i.e. for separated schemes of finite type over a finite field, as stated and proved by Burns and the author. We will also comment briefly on versions of the main conjecture for function fields.

arXiv:1103.3069 An Equivariant Main Conjecture in Iwasawa Theory and Applications from arXiv Front: math.NT by Cornelius Greither, Cristian D. Popescu We construct a new class of Iwasawa modules, which are the number field analogues of the p-adic realizations of the Picard 1-motives constructed by Deligne in the 1970s and studied extensively from a Galois module structure point of view in our recent work. We prove that the new Iwasawa modules are of projective dimension 1 over the appropriate profinite group rings. In the abelian case, we prove an Equivariant Main Conjecture, identifying the first Fitting ideal of the Iwasawa module in question over the appropriate profinite group ring with the principal ideal generated by a certain equivariant p-adic L-function. This is an integral, equivariant refinement of the classical Main Conjecture over totally real number fields proved by Wiles in 1990. Finally, we use these results and Iwasawa co-descent to prove refinements of the (imprimitive) Brumer-Stark Conjecture and the Coates-Sinnott Conjecture, away from their 2-primary components, in the most general number field setting. All of the above is achieved under the assumption that the relevant prime p is odd and that the appropriate classical Iwasawa mu-invariants vanish (as conjectured by Iwasawa.)

arXiv:1109.5525 Equivariant Iwasawa theory and non-abelian Stark-type conjectures from arXiv Front: math.NT by Andreas Nickel We discuss three different formulations of the equivariant Iwasawa main conjecture attached to an extension $\mc K/k$ of totally real fields with Galois group $\mc G$, where $k$ is a number field and $\mc G$ is a $p$-adic Lie group of dimension 1 for an odd prime $p$. All these formulations are equivalent and hold if Iwasawa’s $\mu$-invariant vanishes. Under mild hypotheses, we use this to prove non-abelian generalizations of Brumer’s conjecture, the Brumer-Stark conjecture and a strong version of the Coates-Sinnott conjecture provided that $\mu = 0$.

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Old list of refs:

LMS book on L-functions that Mahesh has

$p$-adic $L$-Functions and $p$-adic Representations. Perrin-Riou

cool article by wojciech gajda: on K… and classical conjectures in the arithmetic of cyclotomic fields. in contemporary mathemtics vol 346

nLab page on Iwasawa theory [private]