125 citations · 250 across the 18 of their papers we have counts for
20 papers
Torsion-vanishing for Siegel modular varieties via supercuspidal congruences
Ana Caraiani, Sug Woo Shin
We prove that the generic part of the cohomology of Siegel modular varieties with torsion coefficients is concentrated above the middle degree, under a suitable notion of genericit…
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…
Recent progress on Langlands reciprocity for : Shimura varieties and beyond
Ana Caraiani, Sug Woo Shin
The goal of these lecture notes is to survey progress on the global Langlands reciprocity conjecture for over number fields from the last decade and a half. We high…
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…
Local geometry of moduli stacks of two-dimensional Galois representations
Ana Caraiani, Matthew Emerton, Toby Gee +1
We construct moduli stacks of two-dimensional mod p representations of the absolute Galois group of a p-adic local field, as well as their resolutions by moduli stacks of two-dimen…
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…
On the étale cohomology of Hilbert modular varieties with torsion coefficients
Ana Caraiani, Matteo Tamiozzo
We study the étale cohomology of Hilbert modular varieties, building on the methods introduced for unitary Shimura varieties in [CS17, CS19]. We obtain the analogous vanishing theo…
Vanishing theorems for Shimura varieties at unipotent level
Ana Caraiani, Daniel R. Gulotta, Christian Johansson
We show that the compactly supported cohomology of Shimura varieties of Hodge type of infinite -level (defined with respect to a Borel subgroup) vanishes above the m…
On the generic part of the cohomology of non-compact unitary Shimura varieties
Ana Caraiani, Peter Scholze
We prove that the generic part of the mod l cohomology of Shimura varieties associated to quasi-split unitary groups of even dimension is concentrated above the middle degree, exte…
Moduli stacks of two-dimensional Galois representations
Ana Caraiani, Matthew Emerton, Toby Gee +1
We construct moduli stacks of two-dimensional mod p representations of the absolute Galois group of a p-adic local field, and relate their geometry to the weight part of Serre's co…
Potential automorphy over CM fields
Patrick B. Allen, Frank Calegari, Ana Caraiani +7
Let be a CM number field. We prove modularity lifting theorems for regular -dimensional Galois representations over without any self-duality condition. We deduce that al…
Shimura varieties at level and Galois representations
Ana Caraiani, Daniel R. Gulotta, Chi-Yun Hsu +4
We show that the compactly supported cohomology of certain or -Shimura varieties with -level vanishes above the middle degree. The…
Patching and the p-adic Langlands program for GL(2, Q_p)
Ana Caraiani, Matthew Emerton, Toby Gee +3
We present a new construction of the p-adic local Langlands correspondence for GL(2, Q_p) via the patching method of Taylor--Wiles and Kisin. This construction sheds light on the r…
Kisin modules with descent data and parahoric local models
Ana Caraiani, Brandon Levin
We construct a moduli space of Kisin modules with tame descent datum and with fixed -adic Hodge type , for some finite extension . We show…
p-adic q-expansion principles on unitary Shimura varieties
Ana Caraiani, Ellen Eischen, Jessica Fintzen +2
We formulate and prove certain vanishing theorems for p-adic automorphic forms on unitary groups of arbitrary signature. The p-adic q-expansion principle for p-adic modular forms o…
On the image of complex conjugation in certain Galois representations
Ana Caraiani, Bao V. Le Hung
We compute the image of any choice of complex conjugation on the Galois representations associated to regular algebraic cuspidal automorphic representations and to torsion classes…
Patching and the p-adic local Langlands correspondence
Ana Caraiani, Matthew Emerton, Toby Gee +3
We use the patching method of Taylor--Wiles and Kisin to construct a candidate for the p-adic local Langlands correspondence for GL_n(F), F a finite extension of Q_p. We use our co…
Monodromy and local-global compatibility for l=p
Ana Caraiani
We strengthen the compatibility between local and global Langlands correspondences for GL_{n} when n is even and l=p. Let L be a CM field and Π a cuspidal automorphic representatio…
Local-global compatibility and the action of monodromy on nearby cycles
Ana Caraiani
We strengthen the local-global compatibility of Langlands correspondences for in the case when is even and . Let be a CM field and be a cuspidal autom…