Results 11 to 20 of about 79 (61)

THE BREUIL–MÉZARD CONJECTURE FOR POTENTIALLY BARSOTTI–TATE REPRESENTATIONS

Forum of Mathematics, Pi, 2014
We prove the Breuil–Mézard conjecture for two-dimensional potentially Barsotti–Tate representations of the absolute Galois group $G_{K}$, $K$ a finite extension of $\mathbb{Q}_{p}$, for any $p>2$ (up to the question of determining precise ...
TOBY GEE, MARK KISIN
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A computational study of the asymptotic behaviour of coefficient fields of modular forms [PDF]

, 2009
The article motivates, presents and describes large computer calculations concerning the asymptotic behaviour of arithmetic properties of coefficient fiel ds of modular forms. The observations suggest certain patterns, which deserve further study.
Marcel Mohyla, Gabor Wiese
semanticscholar   +1 more source

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
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EISENSTEIN–KRONECKER SERIES VIA THE POINCARÉ BUNDLE

Forum of Mathematics, Sigma, 2019
A classical construction of Katz gives a purely algebraic construction of Eisenstein–Kronecker series using the Gauß–Manin connection on the universal elliptic curve. This approach gives a systematic way to study algebraic and $p$-adic properties of real-
JOHANNES SPRANG
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PARALLEL WEIGHT 2 POINTS ON HILBERT MODULAR EIGENVARIETIES AND THE PARITY CONJECTURE

Forum of Mathematics, Sigma, 2019
Let $F$ be a totally real field and let $p$ be an odd prime which is totally split in $F$. We define and study one-dimensional ‘partial’ eigenvarieties interpolating Hilbert modular forms over $F$ with weight varying only at a single place $v$ above $p$.
CHRISTIAN JOHANSSON, JAMES NEWTON
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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
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On Artin representations and nearly ordinary Hecke algebras over totally real fields

Documenta Mathematica, 2013
We prove many new cases of the strong Artin conjecture for two-dimensional, totally odd, insoluble (icosahedral) representations Gal(F/F ) → GL2(C) of the absolute Galois group of a totally real field F .
Shu Sasaki
semanticscholar   +1 more source

THE BERNSTEIN CENTER OF THE CATEGORY OF SMOOTH $W(k)[\text{GL}_{n}(F)]$ -MODULES

Forum of Mathematics, Sigma, 2016
We consider the category of smooth $W(k)[\text{GL}_{n}(F)]$ -modules, where $F$
DAVID HELM
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Raising the level for $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\text {GL}_{{n}}$

Forum of Mathematics, Sigma, 2014
We prove a simple level-raising result for regular algebraic, conjugate self-dual automorphic forms on $\mathrm{GL}_n$ .
JACK A. THORNE
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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
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