Results 21 to 30 of about 624 (65)

Vanishing theorems for the mod p cohomology of some simple Shimura varieties

Forum of Mathematics, Sigma, 2020
We show that the mod p cohomology of a simple Shimura variety treated in Harris-Taylor’s book vanishes outside a certain nontrivial range after localizing at any non-Eisenstein ideal of the Hecke algebra. In cases of low dimensions, we show the vanishing
Teruhisa Koshikawa
doaj   +1 more source

Smith theory and cyclic base change functoriality

Forum of Mathematics, Pi
Lafforgue and Genestier-Lafforgue have constructed the global and (semisimplified) local Langlands correspondences for arbitrary reductive groups over function fields.
Tony Feng
doaj   +1 more source

THE WEIGHT PART OF SERRE’S CONJECTURE FOR $\text{GL}(2)$

Forum of Mathematics, Pi, 2015
Let $p>2$ be prime. We use purely local methods to determine the possible reductions of certain two-dimensional crystalline representations, which we call pseudo-Barsotti–Tate representations, over arbitrary finite extensions of $\mathbb{Q}_{p}$.
TOBY GEE, TONG LIU, DAVID SAVITT
doaj   +1 more source

The Ramanujan and Sato–Tate Conjectures for Bianchi modular forms

Forum of Mathematics, Pi
We prove the Ramanujan and Sato–Tate conjectures for Bianchi modular forms of weight at least $2$ . More generally, we prove these conjectures for all regular algebraic cuspidal automorphic representations of $\operatorname {\mathrm {GL}}_2 ...
George Boxer, Frank Calegari, Toby Gee, James Newton, Jack A. Thorne   +4 more
doaj   +1 more source

Components of moduli stacks of two-dimensional Galois representations

Forum of Mathematics, Sigma
In the article [CEGS20b], we introduced various moduli stacks of two-dimensional tamely potentially Barsotti–Tate representations of the absolute Galois group of a p-adic local field, as well as related moduli stacks of Breuil–Kisin modules with descent ...
Ana Caraiani, Matthew Emerton, Toby Gee, David Savitt   +3 more
doaj   +1 more source

Modularity lifting results in parallel weight one and applications to the Artin conjecture: the tamely ramified case

Forum of Mathematics, Sigma, 2014
We extend the modularity lifting result of P. Kassaei (‘Modularity lifting in parallel weight one’,J. Amer. Math. Soc. 26 (1) (2013), 199–225) to allow Galois representations with some ramification at
PAYMAN L. KASSAEI, SHU SASAKI, YICHAO TIAN   +2 more
doaj   +1 more source

On local Galois deformation rings: generalised tori

Forum of Mathematics, Sigma
We study deformation theory of mod p Galois representations of p-adic fields with values in generalised tori, such as L-groups of (possibly non-split) tori.
Vytautas Paškūnas, Julian Quast
doaj   +1 more source

COMPATIBLE SYSTEMS OF GALOIS REPRESENTATIONS ASSOCIATED TO THE EXCEPTIONAL GROUP $E_{6}$

Forum of Mathematics, Sigma, 2019
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 groups equal to the exceptional group of type $E_{6}$.
GEORGE BOXER, FRANK CALEGARI, MATTHEW EMERTON, BRANDON LEVIN, KEERTHI MADAPUSI PERA, STEFAN PATRIKIS   +5 more
doaj   +1 more source

An irreducibility criterion for group representations, with arithmetic applications

, 2010
We prove a criterion for the irreducibility of an integral group representation \rho over the fraction field of a noetherian domain R in terms of suitably defined reductions of \rho at prime ideals of R.
Longo, M., Vigni, S.
core   +2 more sources

Locally analytic vectors and decompletion in mixed characteristic

Forum of Mathematics, Sigma
In p-adic Hodge theory and the p-adic Langlands program, Banach spaces with $\mathbf {Q}_p$ -coefficients and p-adic Lie group actions are central.
Gal Porat
doaj   +1 more source