26 citations · 52 across the 8 of their papers we have counts for
9 papers
Modularity theorems for abelian surfaces
George Boxer, Frank Calegari, Toby Gee +1
We prove the modularity of a positive proportion of abelian surfaces over . More precisely, we prove the modularity of abelian surfaces which are ordinary at and ar…
p-adic interpolation of Gauss--Manin connections on nearly overconvergent modular forms and p-adic L-functions
Andrew Graham, Vincent Pilloni, Joaquín Rodrigues Jacinto
In this paper, we give a new geometric definition of nearly overconvergent modular forms and -adically interpolate the Gauss-Manin connection on this space. This can be seen as…
Higher Coleman Theory
George Boxer, Vincent Pilloni
We develop local cohomology techniques to study the finite slope part of the coherent cohomology of Shimura varieties. The local cohomology groups we consider are a generalization…
Higher Hida and Coleman theories on the modular curve
George Boxer, Vincent Pilloni
We construct Hida and Coleman theories for the degree 0 and 1 cohomology of automorphic line bundles on the modular curve and we define a p-adic duality pairing between the theorie…
Hecke operators and the coherent cohomology of Shimura varieties
Najmuddin Fakhruddin, Vincent Pilloni
We consider the problem of defining an action of Hecke operators on the coherent cohomology of certain integral models of Shimura varieties. We formulate a general conjecture descr…
Higher Hida theory and p-adic L-functions for GSp(4)
David Loeffler, Vincent Pilloni, Christopher Skinner +1
We use the "higher Hida theory" recently introduced by the second author to p-adically interpolate periods of non-holomorphic automorphic forms for GSp(4), contributing to coherent…
Abelian Surfaces over totally real fields are Potentially Modular
George Boxer, Frank Calegari, Toby Gee +1
We show that abelian surfaces (and consequently curves of genus 2) over totally real fields are potentially modular. As a consequence, we obtain the expected meromorphic continuati…
P-Adic families of Siegel modular cuspforms
Fabrizio Andreatta, Adrain Iovita, Vincent Pilloni
Let p be an odd prime and g an integer greater or equal to 2. We prove that a finite slope Siegel cuspidal eigenform of genus g can be p-adically deformed over the g-dimensional we…
Partial canonical subgroups
Vincent Pilloni, Benoit Stroh
The reduction of Siegel varieties modulo a prime number p is stratified by the multiplicative rank of the p-divisible group of the universal abelian variety. For r\geq 0 the maxima…