8 papers
The Pila-Zannier strategy for Drinfeld modules and Drinfeld modular curves
Gal Binyamini, Dmitry Novikov, Francesco Maria Saettone
We extend the Pila-Zannier strategy to Drinfeld modules: we prove analogues of the Manin-Mumford theorem for a product of two Drinfeld modules of equal rank, and of the André-Oort…
The fundamental group of surfaces parametrizing cuboids
Benjamin Enriquez, David Jarossay, Francesco Maria Saettone +1
We prove that an irreducible projective complete intersection of dimension at least two with isolated singularities has trivial fundamental group. As an application, the surface $Î…
Procounting measures and the Bateman--Horn conjecture
Luca Demangos, Ignazio Longhi, Francesco Maria Saettone
Let be the ring of -integers in a global field and $\da$ its profinite completion. We propose a profinite version of the Bateman--Horn conjecture over and provide a firs…
Duke for Drinfeld
Francesco Maria Saettone
We prove a function field analogue of Duke's equidistribution theorem for CM points, in the setting of Drinfeld--Stuhler modular curves. Our results thus extend, to the Drinfeld se…
A note on equidistribution on a product of Shimura curves and André--Oort
Francesco Maria Saettone
In this short note we show that Galois orbits of CM points equidistribute on a product of non-isomorphic Shimura curves by applying the adelic toral-packet equidistributio…
Polylogarithmic motivic Chabauty-Kim for : the geometric step via resultants
David Jarossay, David T. -B. G. Lilienfeldt, Francesco Maria Saettone +2
Given a finite set of distinct primes, we propose a method to construct polylogarithmic motivic Chabauty-Kim functions for using resul…