The Iwasawa Main Conjectures for GL2

C Skinner, E Urban - Inventiones mathematicae, 2014 - Springer
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Several-variable p-adic families of Siegel-Hilbert cusp eigensystems and their Galois representations

J Tilouine, E Urban - Annales Scientifiques de l'École Normale Supérieure, 1999 - Elsevier
Let F be a totally real field and G= GSp (4)/F. In this paper, we show under a weak
assumption that, given a Hecke eigensystem λ which is (p, P)-ordinary for a fixed parabolic P …

Sur les déformations p-adiques de certaines représentations automorphes

C Skinner, E Urban - Journal of the Institute of Mathematics of …, 2006 - cambridge.org
Résumé Par une méthode entierement nouvelle utilisant les déformations p-adiques de
pentes positives de représentations automorphes pour GSp4/Q, nous prouvons que le p …

Eisenstein congruence on unitary groups and Iwasawa main conjectures for CM fields

ML Hsieh - Journal of the American Mathematical Society, 2014 - ams.org
Eisenstein congruence on unitary groups and Iwasawa main conjectures for CM fields Page 1
JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY Volume 27, Number 3, July 2014 …

Saito–Kurokawa lifts and applications to the Bloch–Kato conjecture

J Brown - Compositio Mathematica, 2007 - cambridge.org
Let f be a newform of weight 2k− 2 and level 1. In this paper we provide evidence for the
Bloch–Kato conjecture for modular forms. We demonstrate an implication that under suitable …

Relating the Tate–Shafarevich group of an elliptic curve with the class group

D Prasad, S Shekhar - Pacific Journal of Mathematics, 2021 - msp.org
The paper formulates a precise relationship between the Tate–Shafarevich group of an
elliptic curve E over ℚ with a quotient of the class group of ℚ (E [p]) on which Gal (ℚ (E [p])∕ …

How can we construct abelian Galois extensions of basic number fields?

B Mazur - Bulletin of the American Mathematical Society, 2011 - ams.org
Irregular primes—37 being the first such prime—have played a great role in number theory.
This article discusses Ken Ribet's construction—for all irregular primes $ p $—of specific …

Siegel modular forms of genus 2 attached to elliptic curves

D Ramakrishnan, F Shahidi - arXiv preprint math/0609468, 2006 - arxiv.org
The object of this article is to construct certain classes of arithmetically significant,
holomorphic Siegel cusp forms F of genus 2, which are neither of Saito-Kurokawa type, in …

Yoshida lifts and Selmer groups

S Böcherer, N Dummigan… - Journal of the …, 2012 - jstage.jst.go.jp
Let f and g, of weights k> k≥ 2, be normalised newforms for Γ0 (N), for square-free N> 1,
such that, for each Atkin-Lehner involution, the eigenvalues of f and g are equal. Let λ| l be a …

Iwasawa–Greenberg main conjecture for nonordinary modular forms and Eisenstein congruences on GU (3, 1)

F Castella, Z Liu, X Wan - Forum of Mathematics, Sigma, 2022 - cambridge.org
In this paper, we prove one divisibility of the Iwasawa–Greenberg main conjecture for the
Rankin–Selberg product of a weight two cusp form and an ordinary complex multiplication …