Results 21 to 30 of about 640 (69)

DERIVED HECKE ALGEBRA AND COHOMOLOGY OF ARITHMETIC GROUPS

Forum of Mathematics, Pi, 2019
We describe a graded extension of the usual Hecke algebra: it acts in a graded fashion on the cohomology of an arithmetic group $\unicode[STIX]{x1D6E4}$.
AKSHAY VENKATESH
doaj   +1 more source

Ordinary Modular Forms and Companion Points on the Eigencurve [PDF]

, 2013
We give a new proof of a result due to Breuil and Emerton which relates the splitting behavior at p of the p-adic Galois representation attached to a p-ordinary modular form to the existence of an overconvergent p-adic companion form for f.Comment: 12 ...
Bergdall, John
core   +4 more sources

Compatible systems of symplectic Galois representations and the inverse Galois problem II. Transvections and huge image. [PDF]

, 2012
This article is the second part of a series of three articles a bout compatible systems of symplectic Galois representations and applications to the inv erse Galois problem.
S. Arias-de-Reyna, L. Dieulefait, G. Wiese   +2 more
semanticscholar   +1 more source

Modularity of the Consani-Scholten quintic. With an appendix by José Burgos Gil and Ariel Pacetti

Documenta Mathematica, 2012
We prove that the Consani-Scholten quintic, a CalabiYau threefold over Q, is Hilbert modular. For this, we refine several techniques known from the context of modular forms.
L. Dieulefait, Ariel Pacetti, M. Schütt
semanticscholar   +1 more source

Higher congruence companion forms [PDF]

, 2012
For a rational prime $p \geq 3$ we consider $p$-ordinary, Hilbert modular newforms $f$ of weight $k\geq 2$ with associated $p$-adic Galois representations $\rho_f$ and $\mod{p^n}$ reductions $\rho_{f,n}$.
Adibhatla, Rajender, Manoharmayum, Jayanta   +1 more
core   +2 more sources

ON THE INTEGRAL HODGE AND TATE CONJECTURES OVER A NUMBER FIELD

Forum of Mathematics, Sigma, 2013
Hassett and Tschinkel gave counterexamples to the integral Hodge conjecture among 3-folds over a number field. We work out their method in detail, showing that essentially all known counterexamples to the integral Hodge conjecture over the complex ...
BURT TOTARO
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

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

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

EULER SYSTEMS FOR HILBERT MODULAR SURFACES

Forum of Mathematics, Sigma, 2018
We construct an Euler system—a compatible family of global cohomology classes—for the Galois representations appearing in the geometry of Hilbert modular surfaces.
ANTONIO LEI, DAVID LOEFFLER, SARAH LIVIA ZERBES   +2 more
doaj   +1 more source