Abstract Recently, Andreatta, Iovita and Pilloni constructed spaces of overconvergent
modular forms in characteristic p, together with a natural extension of the Coleman–Mazur …

Under a stronger genericity condition, we prove the local analogue of ghost conjecture of
Bergdall and Pollack. As applications, we deduce in this case (a) a folklore conjecture of …

Let GG be a connected reductive group over QQ such that G= G/Q _p G= G/Q p is quasi-split,
and let Q ⊂ GQ⊂ G be a parabolic subgroup. We introduce parahoric overconvergent …

We prove a strong form of the trivial zero conjecture at the central point for the p-adic L-
function of a non-critically refined self-dual cohomological cuspidal automorphic …

This is an expository paper on algebraic aspects of exponential sums over finite fields. This
is a new direction. Various examples, results and open problems are presented along the …

We extend Urban's construction of eigenvarieties for reductive groups G such that G (ℝ) has
discrete series to include characteristic p points at the boundary of weight space. In order to …

We prove a strong form of the trivial zero conjecture at the central point for the $ p $-adic $ L
$-function of a non-critically refined self-dual cohomological cuspidal automorphic …

Let F be a totally real field and p be an odd prime which splits completely in F. We prove that
the eigenvariety associated to a definite quaternion algebra over F satisfies the following …

We generalize bounds of Liu-Wan-Xiao for slopes in eigencurves for definite unitary groups
of rank $2 $, which formed the core of their proof of the Coleman-Mazur-Buzzard-Kilford …

We develop a new strategy for studying low weight specializations of p-adic families of
ordinary modular forms. In the elliptic case, we give a new proof of a result of Ghate–Vatsal …