12 citations · 19 across the 9 of their papers we have counts for
10 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…
Semistable abelian varieties over with bad reduction at 19 only: an overview of the Fontaine--Schoof strategy
Francesco Campagna, Pip Goodman
In this paper we provide an overview of a strategy pioneered by Fontaine and heavily refined by Schoof to classify abelian varieties with prescribed bad reduction. Throughout the o…
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…
Ordinary isogeny graphs over : the inverse volcano problem
Henry Bambury, Francesco Campagna, Fabien Pazuki
We give a detailed presentation of -isogeny graphs associated with ordinary elliptic curves defined over . We then focus on the following inverse problem: given…
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…
How big is the image of the Galois representations attached to CM elliptic curves?
Francesco Campagna, Riccardo Pengo
Using an analogue of Serre's open image theorem for elliptic curves with complex multiplication, one can associate to each CM elliptic curve defined over a number field a n…
Effective bounds on differences of singular moduli that are S-units
Francesco Campagna
Given a singular modulus and a set of rational primes , we study the problem of effectively determining the set of singular moduli such that is an -unit. Fo…
Entanglement in the family of division fields of elliptic curves with complex multiplication
Francesco Campagna, Riccardo Pengo
For every elliptic curve which has complex multiplication (CM) and is defined over a number field containing the CM field , we prove that the family of -divi…
Cyclic reduction densities for elliptic curves
Francesco Campagna, Peter Stevenhagen
For an elliptic curve defined over a number field , the heuristic density of the set of primes of for which has cyclic reduction is given by an inclusion-exclusion s…
On singular moduli that are S-units
Francesco Campagna
Recently Yu. Bilu, P. Habegger and L. Kühne proved that no singular modulus can be a unit in the ring of algebraic integers. In this paper we study for which sets S of prime number…