F. Balestrieri

activity

20112026

most citedElliptic fibrations on covers of the elliptic modular surface of level 5

7 citations · 16 across the 13 of their papers we have counts for

collaborators

13 papers

math.AG2026

Refined obstructions to local-global principles for 0-cycles

Francesca Balestrieri, Anouk Greven, Rachel Newton +3

We introduce new `refined' obstructions to local-global principles for 0-cycles on algebraic varieties over number fields. Assuming finiteness of relevant Tate--Shafarevich groups,…

math.NT2025

Counting quadratic points on Fano varieties

Francesca Balestrieri, Kevin Destagnol, Julian Lyczak +2

This paper initiates the systematic study of the number of points of bounded height on symmetric squares of weak Fano varieties. We provide a general framework for establishing the…

math.NT2023

Degrees of closed points on hypersurfaces

Francesca Balestrieri

Let $k$ be any field. Let $X \subset P_{k}^{N}$ be a degree $d \geq 2$ hypersurface. Under some conditions, we prove that if $X (K) \neq = \emptyset$ for some extension $K / k$ wit…

math.NT2023

Campana points on diagonal hypersurfaces

Francesca Balestrieri, Julia Brandes, Miriam Kaesberg +3

We construct an integral model for counting Campana points of bounded height on diagonal hypersurfaces of degree greater than one, and give an asymptotic formula for their number,…

math.NT2022

Descent and étale-Brauer obstructions for 0-cycles

Francesca Balestrieri, Jennifer Berg

For 0-cycles on a variety over a number field, we define an analogue of the classical descent set for rational points. This leads to, among other things, a definition of the étale-…

math.NT2020

First-order theory of a field and its Inverse Galois Problem

Francesca Balestrieri, Jennifer Park, Alexandra Shlapentokh

Let $G$ be a finite group. Then there exists a first-order statement $S (G)$ in the language of rings without parameters and depending only on $G$ such that, for any field $K$ , we h…

math.NT2020

Average Bateman--Horn for Kummer polynomials

Francesca Balestrieri, Nick Rome

For any $r \in N$ and almost all $k \in N$ smaller than $x^{r}$ , we show that the polynomial $f (n) = n^{r} + k$ takes the expected number of prime values as $n$ range…

math.NT2018★ 6 cited

Arithmetic of rational points and zero-cycles on products of Kummer varieties and K3 surfaces

Francesca Balestrieri, Rachel Newton

Let $k$ be a number field. In the spirit of a result by Yongqi Liang, we relate the arithmetic of rational points over finite extensions of $k$ to that of zero-cycles over $k$ for…

math.NT2018

Arithmetic of rational points and zero-cycles on Kummer varieties

Francesca Balestrieri, Rachel Newton

Let $k$ be a number field, let $X$ be a Kummer variety over $k$ , and let $δ$ be an odd integer. In the spirit of a result by Yongqi Liang, we relate the arithmetic of rational poin…

math.AG2017★ 7 cited

Elliptic fibrations on covers of the elliptic modular surface of level 5

Francesca Balestrieri, Julie Desjardins, Alice Garbagnati +3

We consider the K3 surfaces that arise as double covers of the elliptic modular surface of level 5, $R_{5, 5}$ . Such surfaces have a natural elliptic fibration induced by the fibrat…

math.NT2015★ 3 cited

Insufficiency of the Brauer-Manin obstruction for Enriques surfaces

Francesca Balestrieri, Jennifer Berg, Michelle Manes +2

In 2011, Vàrilly-Alvarado and the last author constructed an Enriques surface $X$ over $Q$ with an étale-Brauer obstruction to the Hasse principle and no algebraic Brauer-…

math.NT2013

On Squares in Lucas Sequences

Francesca Balestrieri

In this short paper, we prove, by only using elementary tools, general cases when $U_{n} (P, Q) \neq = □$ , where $U_{n} (P, Q)$ is the Lucas sequence of the first type.

math.GM2011

An equivalent problem to the Twin Prime Conjecture

F. Balestrieri

In this short paper we will show, via elementary arguments, the equivalence of the Twin Prime Conjecture to a problem which might be simpler to prove. Some conclusions are drawn, a…