# Hybrid Iwasawa algebras and the equivariant Iwasawa main conjecture

@article{Johnston2014HybridIA, title={Hybrid Iwasawa algebras and the equivariant Iwasawa main conjecture}, author={Henri Johnston and Henri Nickel}, journal={American Journal of Mathematics}, year={2014}, volume={140}, pages={245 - 276} }

Abstract: Let $p$ be an odd prime. We give an unconditional proof of the equivariant Iwasawa main conjecture for totally real fields for an infinite class of one-dimensional non-abelian $p$-adic Lie extensions. Crucially, this result does not depend on the vanishing of the relevant Iwasawa $\mu$-invariant.

## 11 Citations

An unconditional proof of the abelian equivariant Iwasawa main conjecture and applications

- Mathematics
- 2020

Let $p$ be an odd prime. We give an unconditional proof of the equivariant Iwasawa main conjecture for totally real fields for every admissible one-dimensional $p$-adic Lie extension whose Galois…

On the non-abelian Brumer–Stark conjecture and the equivariant Iwasawa main conjecture

- MathematicsMathematische Zeitschrift
- 2018

We show that for an odd prime p, the p-primary parts of refinements of the (imprimitive) non-abelian Brumer and Brumer–Stark conjectures are implied by the equivariant Iwasawa main conjecture (EIMC)…

Conjectures of Brumer, Gross and Stark

- MathematicsSpectral Structures and Topological Methods in Mathematics
- 2019

We give an introduction to generalisations of conjectures of Brumer and Stark on the annihilator of the class group of a number field. We review the relation to the equivariant Tamagawa number…

Leopoldt-type theorems for non-abelian extensions of Q

- Mathematics
- 2021

We prove new results concerning the additive Galois module structure of certain wildly ramified finite non-abelian extensions of Q. In particular, when K/Q is a Galois extension with Galois group G…

On the non-abelian Brumer-Stark conjecture

- Mathematics
- 2015

We show that for an odd prime p, the p-primary parts of refinements of the (imprimitive) non-abelian Brumer and Brumer-Stark conjectures are implied by the equivariant Iwasawa main conjecture (EIMC)…

On free resolutions of Iwasawa modules

- Mathematics
- 2017

Let $\Lambda$ (isomorphic to $\mathbb{Z}_p[[T]]$) denote the usual Iwasawa algebra and $G$ denote the Galois group of a finite Galois extension $L/K$ of totally real fields. When the non-primitive…

On the p‐adic Stark conjecture at s=1 and applications

- Mathematics
- 2017

Let E/F be a finite Galois extension of totally real number fields and let p be a prime. The `p-adic Stark conjecture at s=1' relates the leading terms at s=1 of p-adic Artin L-functions to those of…

On derivatives of p-adic L-series at s = 0

- Mathematics
- 2018

Abstract We use techniques of non-commutative Iwasawa theory to investigate the values at zero of higher derivatives of p-adic Artin L-series.

On the Theory of Higher Rank Euler, Kolyvagin and Stark Systems

- MathematicsInternational Mathematics Research Notices
- 2019

Mazur and Rubin have recently developed a theory of higher rank Kolyvagin and Stark systems over principal artinian rings and discrete valuation rings. We describe a natural extension of (a…

On the p-adic Beilinson conjecture and the equivariant Tamagawa number conjecture

- MathematicsSelecta Mathematica
- 2021

<jats:p>Let <jats:italic>E</jats:italic>/<jats:italic>K</jats:italic> be a finite Galois extension of totally real number fields with Galois group <jats:italic>G</jats:italic>. Let…

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We show that for an odd prime p, the p-primary parts of refinements of the (imprimitive) non-abelian Brumer and Brumer-Stark conjectures are implied by the equivariant Iwasawa main conjecture (EIMC)…

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