Results 1 to 10 of about 432 (61)

Sturm Bounds for Siegel Modular Forms [PDF]

open access: yesResearch in Number Theory, 2015
We establish Sturm bounds for degree g Siegel modular forms modulo a prime p, which are vital for explicit computations. Our inductive proof exploits Fourier-Jacobi expansions of Siegel modular forms and properties of specializations of Jacobi forms to ...
Richter, Olav K.   +1 more
core   +5 more sources

Overconvergent modular forms are highest-weight vectors in the Hodge-Tate weight zero part of completed cohomology

open access: yesForum of Mathematics, Sigma, 2021
We construct a $(\mathfrak {gl}_2, B(\mathbb {Q}_p))$ and Hecke-equivariant cup product pairing between overconvergent modular forms and the local cohomology at $0$ of a sheaf on $\mathbb {P}^1$, landing in the compactly supported completed $\mathbb {C ...
Sean Howe
doaj   +1 more source

Modular forms of half-integral weight on Γ0(4) with few nonvanishing coefficients modulo ℓ

open access: yesOpen Mathematics, 2022
Let kk be a nonnegative integer. Let KK be a number field and OK{{\mathcal{O}}}_{K} be the ring of integers of KK. Let ℓ≥5\ell \ge 5 be a prime and vv be a prime ideal of OK{{\mathcal{O}}}_{K} over ℓ\ell . Let ff be a modular form of weight k+12k+\frac{1}
Choi Dohoon, Lee Youngmin
doaj   +1 more source

ON THE IRREDUCIBLE COMPONENTS OF SOME CRYSTALLINE DEFORMATION RINGS

open access: yesForum of Mathematics, Sigma, 2020
We adapt a technique of Kisin to construct and study crystalline deformation rings of $G_{K}$ for a finite extension $K/\mathbb{Q}_{p}$. This is done by considering a moduli space of Breuil–Kisin modules, satisfying an additional Galois condition, over ...
ROBIN BARTLETT
doaj   +1 more source

SERRE WEIGHTS AND BREUIL’S LATTICE CONJECTURE IN DIMENSION THREE

open access: yesForum of Mathematics, Pi, 2020
We prove in generic situations that the lattice in a tame type induced by the completed cohomology of a $U(3)$-arithmetic manifold is purely local, that is, only depends on the Galois representation at places above $p$. This is a generalization to $\text{
DANIEL LE   +3 more
doaj   +1 more source

Congruences between modular forms given by the divided $\beta$ family in homotopy theory [PDF]

open access: yes, 2008
We characterize the 2‐line of the p ‐local Adams‐Novikov spectral sequence in terms of modular forms satisfying a certain explicit congruence condition for primes p 5.

semanticscholar   +1 more source

On depth zero L‐packets for classical groups

open access: yesProceedings of the London Mathematical Society, Volume 121, Issue 5, Page 1083-1120, November 2020., 2020
Abstract By computing reducibility points of parabolically induced representations, we construct, to within at most two unramified quadratic characters, the Langlands parameter of an arbitrary depth zero irreducible cuspidal representation π of a classical group (which may be not‐quasi‐split) over a non‐archimedean local field of odd residual ...
Jaime Lust, Shaun Stevens
wiley   +1 more source

2‐adic slopes of Hilbert modular forms over Q(5)

open access: yesBulletin of the London Mathematical Society, Volume 52, Issue 4, Page 716-729, August 2020., 2020
Abstract We show that for arithmetic weights with a fixed finite‐order character, the slopes of Up for p=2 (which is inert) acting on overconvergent Hilbert modular forms of level U0(4) are independent of the (algebraic part of the) weight and can be obtained by a simple recipe from the classical slopes in parallel weight 3.
Christopher Birkbeck
wiley   +1 more source

THE BREUIL–MÉZARD CONJECTURE FOR POTENTIALLY BARSOTTI–TATE REPRESENTATIONS

open access: yesForum 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
doaj   +1 more source

On mod p modular representations which are defined over \F_p [PDF]

open access: yes, 2007
In this paper, we use techniques of Conrey, Farmer and Wallace to find spaces of modular forms $S_k(\Gamma_0(N))$ where all of the eigenspaces have Hecke eigenvalues defined over $\F_p$, and give a heuristic indicating that these are all such spaces ...
Kilford, L. J. P.
core   +5 more sources

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