4 citations · 16 across the 15 of their papers we have counts for
17 papers
Intersecting a curve in an abelian variety with multiples of another curve
Fabrizio Barroero, Gabriel A. Dill, Lars Kuehne
Levin asked what can be said about the locus of points lying on a given curve in that have a non-zero integer multiple on another given curve in f…
Arithmetic unlikely intersections in powers of the multiplicative group
Francesco Campagna, Gabriel Andreas Dill, Robert Wilms
Inspired by work of Bugeaud-Corvaja-Zannier, we formulate a conjecture about unlikely intersections in powers of the multiplicative group over the ring of integers in a number fiel…
New evidence for Rémond's generalisation of Lehmer's conjecture
Sara Checcoli, Gabriel Andreas Dill
In this article, we generalise a result of Pottmeyer from the multiplicative group of the algebraic numbers to almost split semiabelian varieties defined over number fields. This c…
Likely intersections in powers of the multiplicative group
Gabriel Andreas Dill, Francesco Gallinaro
We derive two finiteness properties as consequences of the geometrical non-degeneracy of an algebraic subvariety of a power of the multiplicative group, concerning the intersec…
Hecke orbits and the Mordell-Lang conjecture in distinguished categories
Fabrizio Barroero, Gabriel Andreas Dill
Inspired by recent work of Aslanyan and Daw, we introduce the notion of -orbits in the general framework of distinguished categories. In the setting of connected Shimura varieti…
Algebraic relations over finite fields that preserve the endomorphism rings of CM -invariants
Francesco Campagna, Gabriel Andreas Dill
We characterise the integral affine plane curves over a finite field with the property that all but finitely many of their -points have coordinates that are -i…
On a Galois property of fields generated by the torsion of an abelian variety
Sara Checcoli, Gabriel Andreas Dill
In this article, we study a certain Galois property of subextensions of , the minimal field of definition of all torsion points of an abelian variety defi…
Around the support problem for Hilbert class polynomials
Francesco Campagna, Gabriel Andreas Dill
Let denote the Hilbert class polynomial of the imaginary quadratic order of discriminant . We study the rate of growth of the greatest common divisor of and $H…
On morphisms between connected commutative algebraic groups over a field of characteristic
Gabriel Andreas Dill
Let be a field of characteristic and let and be connected commutative algebraic groups over . Let denote the set of morphisms of algebraic va…
Distinguished categories and the Zilber-Pink conjecture
Fabrizio Barroero, Gabriel Andreas Dill
We propose an axiomatic approach towards studying unlikely intersections by introducing the framework of distinguished categories. This includes commutative algebraic groups and mi…
On the frequency of height values
Gabriel Andreas Dill
We count algebraic numbers of fixed degree and fixed (absolute multiplicative Weil) height with precisely conjugates that lie inside the open unit disk. We al…
Torsion points on isogenous abelian varieties
Gabriel Andreas Dill
Investigating a conjecture of Zannier, we study irreducible subvarieties of abelian schemes that dominate the base and contain a Zariski dense set of torsion points that lie on pai…
On the Zilber-Pink conjecture for complex abelian varieties
Fabrizio Barroero, Gabriel Andreas Dill
In this article, we prove that the Zilber-Pink conjecture for abelian varieties over an arbitrary field of characteristic is implied by the same statement for abelian varieties…
Unlikely intersections with isogeny orbits in a product of elliptic schemes
Gabriel Andreas Dill
Fix an elliptic curve without CM and a non-isotrivial elliptic scheme over a smooth irreducible curve, both defined over the algebraic numbers. Consider the union of all imag…
Generalized Vojta-Rémond inequality
Gabriel Andreas Dill
Following and generalizing unpublished work of Ange, we prove a generalized version of Rémond's generalized Vojta inequality. This generalization can be applied to arbitrary produc…
Unlikely intersections between isogeny orbits and curves
Gabriel Andreas Dill
Fix an abelian variety and a non-isotrivial abelian scheme over a smooth irreducible curve, both defined over the algebraic numbers. Consider the union of all images of trans…
Effective Approximation and Diophantine Applications
Gabriel Andreas Dill
Using the Thue-Siegel method, we obtain effective improvements on Liouville's irrationality measure for certain one-parameter families of algebraic numbers, defined by equations of…