This book (1) takes place in a now thirty years long trend of researches, initiated by Ribet
([95]) aiming at constructing “arithmetically interesting” non trivial extensions between global …

Let $ X $ be a smooth projective variety defined over $\overline {\Bbb {Q}} $, and $ f\colon
X\dashrightarrow X $ be a dominant rational map. Let $\delta_f $ be the first dynamical …

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 …

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 …

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 …

We study short crystalline, minimal, essentially self-dual deformations of a mod $ p $ non-
semisimple Galois representation $\overline {\sigma} $ with $\overline {\sigma}^{{\rm …

We introduce a new method of proof for R= T theorems in the residually reducible case. We
study the crystalline universal deformation ring R (and its ideal of reducibility I) of a mod p …

In this paper, we first characterize the subsets of the Bruhat–Tits tree of PGL 2 (K), K a
complete valued field, that are the sets of fixed points C (G) of a subgroup G of GL 2 (K) …

Let k> 9 be an even integer and pa prime with p> 2k− 2. Let f be a newform of weight 2k− 2
and level \mathrmSL_2(\mathbbZ) so that f is ordinary at p and \overlineρ_f,\mathfrakp is …

Let K be a finite extension of the p-adic field ${\mathbb {Q}} _p $ of degree d, let ${{\mathbb
{F}}\,\!{}} $ be a finite field of characteristic p and let ${\overline {{D}}} $ be an n-dimensional …