The Iwasawa Main Conjectures for GL2
@article{Skinner2014TheIM,
title={The Iwasawa Main Conjectures for GL2},
author={Christopher Skinner and Eric Urban},
journal={Inventiones mathematicae},
year={2014},
volume={195},
pages={1-277},
url={https://api.semanticscholar.org/CorpusID:120848645}
}We prove the one-, two-, and three-variable Iwasawa-Greenberg Main Conjectures for a large class of modular forms that are ordinary with respect to an odd prime p. The method of proof involves an analysis of an Eisenstein ideal for ordinary Hida families for GU(2,2).
304 Citations
Iwasawa Main Conjecture for Non-Ordinary Modular Forms
- 2016
Mathematics
Let $p>2$ be a prime. Under mild assumptions, we prove the Iwasawa main conjecture of Kato, for modular forms with general weight and conductor prime to $p$. This generalizes an earlier work of the…
Iwasawa Main Conjecture for Non-Ordinary Modular Forms
- 2017
Mathematics
Let p > 2 be a prime. Under mild assumptions, we prove the Iwasawa main conjecture of Kato, for modular forms with general weight and conductor prime to p. This generalizes an earlier work of the…
Multiplicative reduction and the cyclotomic main conjecture for GL2
- 2016
Mathematics
We show that the cyclotomic Iwasawa--Greenberg Main Conjecture holds for a large class of modular forms with multiplicative reduction at $p$, extending previous results for the good ordinary case. In…
Eisenstein congruence on unitary groups and Iwasawa main conjectures for CM fields
- 2014
Mathematics
The purpose of this article is to prove Iwasawa main conjecture for CM fields in certain cases through an extensive study on the divisibility relation between p-adic L-functions for CM fields and…
THE IWASAWA MAIN CONJECTURES FOR GL2 AND DERIVATIVES OF p-ADIC L-FUNCTIONS
- 2020
Mathematics
We prove under mild hypotheses the three-variable Iwasawa Main Conjecture for p-ordinary modular forms base changed to an imaginary quadratic field K in which p splits in the indefinite setting (in…
Wall crossing in Iwasawa theory
- 2024
Mathematics
This paper sets up a framework to organize anticyclotomic Iwasawa theory in the context of the Gan-Gross-Prasad conjecture for unitary groups. We propose multiple main conjectures depending on…
On the anticyclotomic Iwasawa main conjecture for modular forms
- 2014
Mathematics
We generalize the work of Bertolini and Darmon on the anticyclotomic main conjecture for elliptic curves to modular forms of higher weight.
An archimedian analog of Iwasawa theory
- 2012
Mathematics
We will show a conjecture which reduces Mazur-Tate-Teitelbaum conjecture to the known cases. In order to explain its background we will develop an archimedian analog of Iwasawa theory. Moreover…
THE IWASAWA MAIN CONJECTURE FOR HILBERT MODULAR FORMS
- 2015
Mathematics
Following the ideas and methods of a recent work of Skinner and Urban, we prove the one divisibility of the Iwasawa main conjecture for nearly ordinary Hilbert modular forms under certain local…
84 References
Iwasawa theory for elliptic curves
- 1999
Mathematics
We study this subject by first proving that the p-primary subgroup of the classical Selmer group for an elliptic curve with good, ordinary reduction at a prime p has a very simple and elegant…
On the two-variable Iwasawa main conjecture
- 2006
Mathematics
This paper is a continuation of the author's previous work, where we studied one of the inequalities between the characteristic ideal of the Selmer group and the ideal of the $p$-adic $L$-function…
The structure of Selmer groups.
- 1997
Mathematics
Under certain hypotheses, one can prove the nonexistence of proper Lambda-submodules of finite index in Selmer groups under the Weak Leopoldt Conjecture.
On p-adic L-functions and cyclotomic fields
- 1975
Mathematics
Let p be a prime. If one adjoins to Q all pn -th roots of unity for n = 1, 2, 3, …, then the resulting field will contain a unique subfield Q ∞ such that Q ∞ is a Galois extension of Q with Gal the…
Selmer groups and the Eisenstein-Klingen ideal
- 1998
Mathematics
In this article, we set up a strategy to prove one divisibility towards the main Iwasawa conjecture for the Selmer groups attached to the twisted adjoint modular Galois representations associated to…
On the Iwasawa invariants of elliptic curves
- 2000
Mathematics
Let p be an odd prime. Suppose that E is a modular elliptic curve/Q with good ordinary reduction at p. Let Q_{oo} denote the cyclotomic Z_p-extension of Q. It is conjectured that Sel_E(Q_{oo}) is a…
NON-ARCHIMEDEAN MEASURES CONNECTED WITH DIRICHLET SERIES
- 1976
Mathematics
In this paper we construct p-adic Hecke series which correspond to cusp forms for congruence subgroups. We give a construction of complex-valued measures on the Galois group which are connected with…
Galois Representations in Arithmetic Algebraic Geometry: On the Satake isomorphism
- 1998
Mathematics
In this paper, we present an expository treatment of the Satake transform. This gives an isomorphism between the spherical Hecke algebra of a split reductive group G over a local field and the…
Several-variable p-adic families of Siegel-Hilbert cusp eigensystems and their Galois representations
- 1999
Mathematics
Degeneration of Abelian varieties
- 1990
Mathematics
I. Preliminaries.- II. Degeneration of Polarized Abelian Varieties.- III. Mumford's Construction.- IV. Toroidal Compactification of Ag.- V. Modular Forms and the Minimal Compactification.- VI.…