6 papers
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 variet…
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 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…