Galois representations arising from some compact Shimura varieties
SW Shin - Annals of mathematics, 2011 - JSTOR
Our aim is to establish some new cases of the global Langlands correspondence for GLm.
Along the way we obtain a new result on the description of the cohomology of some compact …
Along the way we obtain a new result on the description of the cohomology of some compact …
Level-raising and symmetric power functoriality, I
L Clozel, JA Thorne - Compositio Mathematica, 2014 - cambridge.org
COMPOSITIO MATHEMATICA Page 1 COMPOSITIO MATHEMATICA Compositio Math. doi:10.1112/S0010437X13007653
FOUNDATION COMPOSITIO MATHEMATICA 150 (2014), Level-raising and symmetric …
FOUNDATION COMPOSITIO MATHEMATICA 150 (2014), Level-raising and symmetric …
Level raising and symmetric power functoriality, II
L Clozel, JA Thorne - Annals of Mathematics, 2015 - JSTOR
We apply automorphy lifting techniques to establish new cases of symmetric power
functoriality for Hilbert modular forms of regular algebraic weight. The proof is based on a …
functoriality for Hilbert modular forms of regular algebraic weight. The proof is based on a …
Level-raising and symmetric power functoriality, III
L Clozel, JA Thorne - 2017 - projecteuclid.org
The simplest case of the Langlands functoriality principle asserts the existence of the
symmetric powers Sym n of a cuspidal representation of GL (2) over the adèles of F, where F …
symmetric powers Sym n of a cuspidal representation of GL (2) over the adèles of F, where F …
The refined Gross–Prasad conjecture for unitary groups
RN Harris - International Mathematics Research Notices, 2014 - ieeexplore.ieee.org
Let F be a number field and \mathbbA_F be its ring of adèles, and let π n and π n+ 1 be
irreducible, cuspidal, automorphic representations of \rmSO_n(\mathbbA_F) and …
irreducible, cuspidal, automorphic representations of \rmSO_n(\mathbbA_F) and …
Torsion Galois representations over CM fields and Hecke algebras in the derived category
J Newton, JA Thorne - Forum of Mathematics, Sigma, 2016 - cambridge.org
We construct algebras of endomorphisms in the derived category of the cohomology of
arithmetic manifolds, which are generated by Hecke operators. We construct Galois …
arithmetic manifolds, which are generated by Hecke operators. We construct Galois …
p-adic cohomology and classicality of overconvergent Hilbert modular forms
Y Tian, L Xiao - arXiv preprint arXiv:1308.0779, 2013 - arxiv.org
Let $ F $ be a totally real field in which $ p $ is unramified. We prove that, if a cuspidal
overconvergent Hilbert cuspidal form has small slopes under $ U_p $-operators, then it is …
overconvergent Hilbert cuspidal form has small slopes under $ U_p $-operators, then it is …
On constructing zeta elements for Shimura varieties
SWA Shah - arXiv preprint arXiv:2409.03517, 2024 - arxiv.org
We present a novel axiomatic framework for establishing horizontal norm relations in Euler
systems that are built from pushforwards of classes in the motivic cohomology of Shimura …
systems that are built from pushforwards of classes in the motivic cohomology of Shimura …
On Goren–Oort stratification for quaternionic Shimura varieties
Y Tian, L Xiao - Compositio Mathematica, 2016 - cambridge.org
Let F be a totally real field in which a prime p is unramified. We define the Goren–Oort
stratification of the characteristic-p fiber of a quaternionic Shimura variety of maximal level at …
stratification of the characteristic-p fiber of a quaternionic Shimura variety of maximal level at …
Ramanujan Complexes and Golden Gates in PU(3)
S Evra, O Parzanchevski - Geometric and Functional Analysis, 2022 - Springer
In a seminal series of papers from the 80's, Lubotzky, Phillips and Sarnak applied the
Ramanujan–Petersson Conjecture for GL 2 (Deligne's theorem), to a special family of …
Ramanujan–Petersson Conjecture for GL 2 (Deligne's theorem), to a special family of …