Publications
14 results found
Allen PB, Calegari F, Caraiani A, et al., 2022, Potential automorphy over CM fields, Publisher: arXiv
Let $F$ be a CM number field. We prove modularity lifting theorems forregular $n$-dimensional Galois representations over $F$ without anyself-duality condition. We deduce that all elliptic curves $E$ over $F$ arepotentially modular, and furthermore satisfy the Sato--Tate conjecture. As anapplication of a different sort, we also prove the Ramanujan Conjecture forweight zero cuspidal automorphic representations for$\mathrm{GL}_2(\mathbf{A}_F)$.
Caraiani A, Gulotta D, Johansson C, 2021, Vanishing theorems for Shimura varieties at unipotent level, Journal of the European Mathematical Society, ISSN: 1435-9855
We show that the compactly supported cohomology of Shimura varieties of Hodge type of infinite Γ1(p∞)-level (defined with respect to a Borel subgroup) vanishes above the middle degree, under the assumption that the group of the Shimura datum splits at p. This generalizes and strengthens the vanishing result proved in "Shimura varieties at level Γ1(p∞) and Galois representations". As an application of this vanishing theorem, we prove a result on the codimensions of ordinary completed homology for the same groups, analogous to conjectures of Calegari--Emerton for completed (Borel--Moore) homology.
Caraiani A, Gulotta DR, Hsu C-Y, et al., 2020, Shimura varieties at level $Γ_1(p^\infty)$ and Galois representations, Compositio Mathematica, Vol: 156, Pages: 1152-1230, ISSN: 0010-437X
We show that the compactly supported cohomology of certain $\mathrm{U}(n,n)$or $\mathrm{Sp}(2n)$-Shimura varieties with $\Gamma_1(p^\infty)$-level vanishesabove the middle degree. The only assumption is that we work over a CM field$F$ in which the prime $p$ splits completely. We also give an application toGalois representations for torsion in the cohomology of the locally symmetricspaces for $\mathrm{GL}_n/F$. More precisely, we use the vanishing result forShimura varieties to eliminate the nilpotent ideal in the construction of theseGalois representations. This strengthens recent results of Scholze andNewton-Thorne.
Caraiani A, Gulotta DR, Johansson C, 2019, Vanishing theorems for Shimura varieties at unipotent level, Publisher: arXiv
We show that the compactly supported cohomology of Shimura varieties of Hodgetype of infinite $\Gamma_1(p^\infty)$-level (defined with respect to a Borelsubgroup) vanishes above the middle degree, under the assumption that the groupof the Shimura datum splits at $p$. This generalizes and strengthens thevanishing result proved in "Shimura varieties at level $\Gamma_1(p^\infty)$ andGalois representations". As an application of this vanishing theorem, we provea result on the codimensions of ordinary completed homology for the samegroups, analogous to conjectures of Calegari--Emerton for completed(Borel--Moore) homology.
Caraiani A, Emerton M, Gee T, et al., 2019, Moduli stacks of two-dimensional Galois representations
We construct moduli stacks of two-dimensional mod p representations of theabsolute Galois group of a p-adic local field, and relate their geometry to theweight part of Serre's conjecture for GL(2).
Caraiani A, Emerton M, Gee T, et al., 2018, Patching and the p-adic Langlands program for GL(2)(Q(p)), Compositio Mathematica, Vol: 154, Pages: 503-548, ISSN: 0010-437X
We present a new construction of the -adic local Langlands correspondence for via the patching method of Taylor–Wiles and Kisin. This construction sheds light on the relationship between the various other approaches to both the local and the global aspects of the -adic Langlands program; in particular, it gives a new proof of many cases of the second author’s local–global compatibility theorem and relaxes a hypothesis on the local mod representation in that theorem.
Caraiani A, Levin B, 2018, KISIN MODULES WITH DESCENT DATA AND PARAHORIC LOCAL MODELS, ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE, Vol: 51, Pages: 181-213, ISSN: 0012-9593
Caraiani A, Scholze P, 2017, On the generic part of the cohomology of compact unitary Shimura varieties, Annals of Mathematics, Vol: 186, Pages: 649-766, ISSN: 0003-486X
The goal of this paper is to show that the cohomology of compactunitary Shimura varieties is concentrated in the middle degree and torsion-free,after localizing at a maximal ideal of the Hecke algebra satisfying a suitablegenericity assumption. Along the way, we establish variousfoundational resultson the geometry of the Hodge-Tate period map. In particular,we compare thefibres of the Hodge-Tate period map with Igusa varieties.
Caraiani A, Emerton M, Gee T, et al., 2016, Patching and the p-adic local Langlands correspondence, Cambridge Journal of Mathematics, Vol: 4, Pages: 197-287, ISSN: 2168-0930
We use the patching method of Taylor–Wiles and Kisin to construct a candidate for the pp-adic local Langlands correspondence for GLn(F)GLn(F), FF a finite extension of QpQp. We use our construction to prove many new cases of the Breuil–Schneider conjecture.
Caraiani A, Le Hung BV, 2016, On the image of complex conjugation in certain Galois representations, Compositio Mathematica, Vol: 152, Pages: 1476-1488, ISSN: 0010-437X
Caraiani A, Eischen E, Fintzen J, et al., 2016, <i>p</i>-Adic <i>q</i>-Expansion Principles on Unitary Shimura Varieties, DIRECTIONS IN NUMBER THEORY, Vol: 3, Pages: 197-243, ISSN: 2364-5733
- Author Web Link
- Cite
- Citations: 6
Caraiani A, 2014, Monodromy and local-global compatibility for <i>l</i> = <i>p</i>, ALGEBRA & NUMBER THEORY, Vol: 8, Pages: 1597-1646, ISSN: 1937-0652
- Author Web Link
- Cite
- Citations: 37
Caraiani A, 2012, LOCAL-GLOBAL COMPATIBILITY AND THE ACTION OF MONODROMY ON NEARBY CYCLES, DUKE MATHEMATICAL JOURNAL, Vol: 161, Pages: 2311-2413, ISSN: 0012-7094
- Author Web Link
- Cite
- Citations: 62
Caraiani A, 2010, Multiplicative semigroups related to the 3<i>x</i>+1 problem, ADVANCES IN APPLIED MATHEMATICS, Vol: 45, Pages: 373-389, ISSN: 0196-8858
- Author Web Link
- Cite
- Citations: 1
This data is extracted from the Web of Science and reproduced under a licence from Thomson Reuters. You may not copy or re-distribute this data in whole or in part without the written consent of the Science business of Thomson Reuters.