28 citations · 45 across the 4 of their papers we have counts for
5 papers · 1 filter
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…
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…
Compatible systems of Galois representations associated to the exceptional group E6
George Boxer, Frank Calegari, Matthew Emerton +3
We construct, over any CM field, compatible systems of l-adic Galois representations that appear in the cohomology of algebraic varieties and have (for all l) algebraic monodromy g…
Torsion in the Coherent Cohomology of Shimura Varieties and Galois Representations
George Boxer
We introduce a method for producing congruences between Hecke eigenclasses, possibly torsion, in the coherent cohomology of automorphic vector bundles on certain good reduction Shi…