Results 11 to 20 of about 450 (80)

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
doaj   +1 more source

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, G. Wiese
semanticscholar   +1 more source

On the freeness of anticyclotomic selmer groups of modular forms [PDF]

, 2016
We establish the freeness of certain anticyclotomic Selmer groups of modular forms. The freeness of these Selmer groups plays a key role in the Euler system arguments introduced by Bertolini and Darmon in their work on the anticyclotomic main conjecture ...
Kim, C., Pollack, R., Weston, T.
core   +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 cubic multisections of Eisenstein series [PDF]

, 2013
A systematic procedure for generating cubic multisections of Eisenstein series is given. The relevant series are determined from Fourier expansions for Eisenstein series by restricting the congruence class of the summation index modulo three.
Alaniz, Andrew, Huber, Tim
core   +3 more sources

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
doaj   +1 more source

Mock theta functions and weakly holomorphic modular forms modulo 2 and 3 [PDF]

, 2013
We prove that the coefficients of certain mock theta functions possess no linear congruences modulo 3. We prove similar results for the moduli 2 and 3 for a wide class of weakly holomorphic modular forms and discuss applications.
Ahlgren, Scott, Kim, Byungchan
core   +1 more source

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
doaj   +1 more source

Dihedral Group, 4-Torsion on an Elliptic Curve, and a Peculiar Eigenform Modulo 4 [PDF]

, 2018
We work out a non-trivial example of lifting a so-called weak eigenform to a true, characteristic 0 eigenform. The weak eigenform is closely related to Ramanujan's tau function whereas the characteristic 0 eigenform is attached to an elliptic curve ...
Kiming, Ian, Rustom, Nadim
core   +3 more sources

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