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 …

Let K be an imaginary quadratic field with discriminant− D. We denote by 𝒪 the ring of
integers of K. Let χ be the primitive Dirichlet character corresponding to K/ℚ. Let be the …

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

Let f1 (resp. f2) denote two (elliptic) newforms of prime level N, trivial character and weight 2
(resp. k+ 2, where k∈{8, 12}). We provide evidence for the Bloch–Kato conjecture for the …

For certain algebraic Hecke characters χ of an imaginary quadratic field F we define an
Eisenstein ideal in a p-adic Hecke algebra acting on cuspidal automorphic forms of GL2/F …

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 …

DK) be an imaginary quadratic field of discriminant− DK. We introduce a notion of an adelic
Maass space SM k,− k/2 for automorphic forms on the quasi-split unitary group U (2, 2) …

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 …

We prove a commutative algebra result which has consequences for congruences between
automorphic forms modulo prime powers. If C denotes the congruence module for a fixed …

In this paper, we study Fontaine-Laffaille, self-dual deformations of a mod p non-semisimple
Galois representation of dimension n with its Jordan-Holder factors being three mutually non …