Results 11 to 20 of about 244 (45)
UNRAMIFIEDNESS OF GALOIS REPRESENTATIONS ARISING FROM HILBERT MODULAR SURFACES
Forum of Mathematics, Sigma, 2017 Let $p$ be a prime number and $F$ a totally real number ...
MATTHEW EMERTON +2 more
doaj +1 more source
On a variation of the Erdős–Selfridge superelliptic curve
Bulletin of the London Mathematical Society, Volume 51, Issue 4, Page 633-638, August 2019., 2019 Abstract In a recent paper by Das, Laishram and Saradha, it was shown that if there exists a rational solution of yl=(x+1)…(x+i−1)(x+i+1)…(x+k) for i not too close to k/2 and y≠0, then logl<3k. In this paper, we extend the number of terms that can be missing in the equation and remove the condition on i.
Sam Edis
wiley +1 more source
COMPUTING IMAGES OF GALOIS REPRESENTATIONS ATTACHED TO ELLIPTIC CURVES
Forum of Mathematics, Sigma, 2016 Let $E$ be an elliptic curve without complex multiplication (CM) over a number field $K$
ANDREW V. SUTHERLAND
doaj +1 more source
, 2011 The notion of adequate subgroups was introduced by Jack Thorne. It is a weakening of the notion of big subgroup used by Wiles and Taylor in proving automorphy lifting theorems for certain Galois representations.
Guralnick, Robert
core +2 more sources
Strong modularity of reducible Galois representations [PDF]
, 2016 In this paper, we call strongly modular those reducible semi-simple odd mod $l$ Galois representations for which the conclusion of the strongest form of Serre's original modularity conjecture holds.
Billerey, Nicolas, Menares, Ricardo
core +4 more sources
Rational points on Erdős–Selfridge superelliptic curves [PDF]
, 2015 Given k⩾2k⩾2, we show that there are at most finitely many rational numbers xx and y≠0y≠0 and integers ℓ⩾2ℓ⩾2 (with (k,ℓ)≠(2,2)(k,ℓ)≠(2,2)) for which $$\begin{eqnarray}x(x+1)\cdots (x+k-1)=y^{\ell }.\end{eqnarray}$$ In particular, if we assume that ℓℓ is
Darmon +6 more
core +2 more sources
On the modularity of reducible mod l Galois representations [PDF]
, 2016 We prove that every odd semisimple reducible (2-dimensional) mod l Galois representation arises from a cuspidal eigenform. In addition, we investigate the possible different types (level, weight, character) of such a modular form. When the representation
Billerey, Nicolas, Menares, Ricardo
core +1 more source
Coleman maps and the p-adic regulator [PDF]
, 2010 This paper is a sequel to our earlier paper "Wach modules and Iwasawa theory for modular forms" (arXiv: 0912.1263), where we defined a family of Coleman maps for a crystalline representation of the Galois group of Qp with nonnegative Hodge-Tate weights ...
Amice +10 more
core +1 more source
Ramification and moduli spaces of finite flat models [PDF]
, 2010 We determine the type of the zeta functions and the range of the dimensions of the moduli spaces of finite flat models of two-dimensional local Galois representations over finite fields.
Imai, Naoki
core +2 more sources
Residual Representations of Semistable Principally Polarized Abelian Varieties [PDF]
, 2016 Let $A$ be a semistable principally polarized abelian variety of dimension $d$ defined over the rationals. Let $\ell$ be a prime and let $\bar{\rho}_{A,\ell} : G_{\mathbb{Q}} \rightarrow \mathrm{GSp}_{2d}(\mathbb{F}_\ell)$ be the representation giving ...
Anni, Samuele +2 more
core +4 more sources