4 papers
Intersection Cohomology of Igusa Stacks
Ana Caraiani, Linus Hamann, Mingjia Zhang
We study the intersection cohomology of minimally compactified Shimura varieties of PEL type AC using Igusa stacks and the work of Fargues-Scholze. More precisely, we construct a s…
On the modularity of elliptic curves over imaginary quadratic fields
Ana Caraiani, James Newton
In this paper, we establish the modularity of every elliptic curve , where runs over infinitely many imaginary quadratic fields, including for $d=1…
Components of moduli stacks of two-dimensional Galois representations
Ana Caraiani, Matthew Emerton, Toby Gee +1
In a previous article we introduced various moduli stacks of two-dimensional tamely potentially Barsotti-Tate representations of the absolute Galois group of a p-adic local field,…
The geometric Breuil-Mézard conjecture for two-dimensional potentially Barsotti-Tate Galois representations
Ana Caraiani, Matthew Emerton, Toby Gee +1
We establish a geometrisation of the Breuil-Mézard conjecture for potentially Barsotti-Tate representations, as well as of the weight part of Serre's conjecture, for moduli stacks…