36 citations · 134 across the 27 of their papers we have counts for
34 papers
Serre's uniformity question and proper subgroups of
Lorenzo Furio, Davide Lombardo
Serre's uniformity question asks whether there exists a bound such that, for every non-CM elliptic curve over and every prime , the residual Galois repr…
Monodromy groups of Jacobians with definite quaternionic multiplication
Victoria Cantoral-Farfán, Davide Lombardo, John Voight
Let be an abelian variety over a number field. The connected monodromy field of is the minimal field over which the images of all the -adic torsion representations ha…
The semi-infinite cohomology of Weyl modules with two singular points
Giorgia Fortuna, Davide Lombardo, Andrea Maffei +1
In their study of spherical representations of an affine Lie algebra at the critical level and of unramified opers, Frenkel and Gaitsgory introduced what they called the Weyl modul…
A family of quintic Thue equations via Skolem's -adic method
Davide Lombardo
In this semi-expository article we solve the diophantine equation for all integers . This gives an example of a family of quintic Thue…
Torsion bounds for a fixed abelian variety and varying number field
Samuel Le Fourn, Davide Lombardo, David Zywina
Let be an abelian variety defined over a number field . For a finite extension , the cardinality of the group of torsion points in c…
On the local-global principle for isogenies of abelian surfaces
Davide Lombardo, Matteo Verzobio
Let be a prime number. We classify the subgroups of and that act irreducibly on $\mathbb{F…
Non-isogenous abelian varieties sharing the same division fields
Davide Lombardo
Two abelian varieties over a number field are called strongly iso-Kummerian if the torsion fields and coincide for all . For all $g…
Some uniform bounds for elliptic curves over
Davide Lombardo, Sebastiano Tronto
We give explicit uniform bounds for several quantities relevant to the study of Galois representations attached to elliptic curves . We consider in particular the subg…
Local opers with two singularities: the case of
Giorgia Fortuna, Davide Lombardo, Andrea Maffei +1
We study local opers with two singularities for the case of the Lie algebra sl(2), and discuss their connection with a two-variables extension of the affine Lie algebra. We prove a…
On the distribution of rational points on ramified covers of abelian varieties
Pietro Corvaja, Julian Lawrence Demeio, Ariyan Javanpeykar +2
We prove new results on the distribution of rational points on ramified covers of abelian varieties over finitely generated fields of characteristic zero. For example, given a…
Cohomology of groups acting on vector spaces over finite fields
Davide Lombardo, Laura Paladino
Let be the finite field with elements and be a subgroup of . A famous theorem of Nori published in 1987 states that there…
How far is an extension of -adic fields from having a normal integral basis?
Ilaria Del Corso, Fabio Ferri, Davide Lombardo
Let be a finite Galois extension of -adic fields with group . It is well-known that contains a free -submodule of finite index. We stu…
Decomposing Jacobians via Galois covers
Davide Lombardo, Elisa Lorenzo García, Christophe Ritzenthaler +1
Let be a (possibly ramified) cover between two algebraic curves of positive genus. We develop tools that may identify the Prym variety of , up to isogeny, a…
Explicit Kummer Theory for Elliptic Curves
Davide Lombardo, Sebastiano Tronto
Let be an elliptic curve defined over a number field , let be a point of infinite order, and let be the set of -division points of in $E(\bar{K}…
Identifying central endomorphisms of an abelian variety via Frobenius endomorphisms
Edgar Costa, Davide Lombardo, John Voight
Assuming the Mumford-Tate conjecture, we show that the center of the endomorphism ring of an abelian variety defined over a number field can be recovered from an appropriate inters…
On the -polynomials of curves over finite fields
Francesco Ballini, Davide Lombardo, Matteo Verzobio
We discuss, in a non-Archimedean setting, the distribution of the coefficients of -polynomials of curves of genus over . Among other results, this allows us to…
Abelian varieties as automorphism groups of smooth projective varieties
Davide Lombardo, Andrea Maffei
We determine which complex abelian varieties can be realized as the automorphism group of a smooth projective variety.
Non-geometric fluxes & tadpole conditions for exotic branes
Davide M. Lombardo, Fabio Riccioni, Stefano Risoli
We extend the -flux analysis carried out recently on the type-II orientifold model to include all the possible non-geometric fluxes. By…
Reductions of points on algebraic groups
Davide Lombardo, Antonella Perucca
Let be the product of an abelian variety and a torus defined over a number field . Fix some prime number . If is a point of infinite order, we consider the…
The 1-eigenspace for matrices in
Davide Lombardo, Antonella Perucca
Fix some prime number and consider an open subgroup either of or of the normalizer of a Cartan subgroup of $\operatorname{GL}_2(\m…
All-optical switching via four-wave mixing Bragg scattering in a silicon platform
Yun Zhao, David Lombardo, Jay Mathews +1
We employ the process of non-degenerate four-wave mixing Bragg scattering (FWM-BS) to demonstrate all-optical control in a silicon platform. In our configuration, a strong, non-inf…
Computing twists of hyperelliptic curves
Davide Lombardo, Elisa Lorenzo García
We give an efficient algorithm to compute equations of twists of hyperelliptic curves of arbitrary genus over any separable field (of characteristic different from 2), and we expli…
Computing the geometric endomorphism ring of a genus 2 Jacobian
Davide Lombardo
We describe an algorithm, based on the properties of the characteristic polynomials of Frobenius, to compute when is the Jacobian of a ni…
fluxes and exotic branes
Davide M. Lombardo, Fabio Riccioni, Stefano Risoli
We consider the superpotential generated in type-II orientifold models by non-geometric fluxes. In particular, we focus on the family of fluxes, that are related b…