J. Voloch

collaborators

8 papers

math.NT2026

Rational points on smooth surfaces in $P^{3}$ over finite fields

Yves Aubry, JosÃ© Felipe Voloch

We improve a bound due to the second author on number of rational points on smooth surfaces in $P^{3}$ over finite fields and look at families of surfaces that achieve or ne…

math.NT2026

Doubly isogenous curves of genus two with a rational action of $D_{6}$

Jeremy Booher, Everett W. Howe, Andrew V. Sutherland +1

Let $C$ and $C^{'}$ be curves over a finite field $K$ , provided with embeddings $I^^{1}$ and $Î¹'$ into their Jacobian varieties. Let $D \to C$ and $D^{'} \to C^{'}$ be the pullbacks (via these e…

math.CO2026

Algebraic capsets

Cassie Grace, JosÃ© Felipe Voloch

Capsets are subsets of $F_{3}^{n}$ with no three points on a line and a capset is complete if it is not a subset of a larger capset. We study some new constructions of capsets…

math.CO2025

Subsets of P^4 with no four points on a plane

Geertrui Van de Voorde, JosÃ© Felipe Voloch

We describe a new construction of a subset of P^4 with no four points on a plane over any finite field of order q in which 3 is not a square. This set has size 2q + 1, is maximal w…

math.NT2025

The p-adic distance of special points to subvarieties

In a paper of Tate and the author, we conjectured a uniform bound for the p-adic distance of torsion points on a semiabelian variety, not lying in a subvariety, to that subvariety.…

math.AG2025

New unlikely intersections on elliptic surfaces

Consider a Jacobian elliptic surface $E \to C$ with a section $P$ of infinite order. Previous work of the first author and UrzÃºa over the complex numbers gives a bound on the numb…