Brendan Creutz

activity

20242026

collaborators

5 papers

math.NT2026

Explicit Brauer-Manin obstructions on plane quartics

Nils Bruin, Brendan Creutz

We describe a method to show a plane quartic over a number field has no rational points. The method can be adapted to show that a curve does not have divisors of degree 1 or 2 and…

math.NT2025

Adelic Mordell-Lang and the Brauer-Manin obstruction

Brendan Creutz

Let $X$ be a closed subvariety of an abelian variety $A$ over a global function field $k$ such that the base change of $A$ to an algebraic closure does not have any positive dimens…

math.NT2025

Quartic del Pezzo surfaces without quadratic points

Brendan Creutz, Bianca Viray

Previous work of the authors showed that every quartic del Pezzo surface over a number field has index dividing $2$ (i.e., has a closed point of degree $2$ modulo $4$ ),, and asked…

math.NT2024

Galois invariants of finite abelian descent and Brauer sets

Brendan Creutz, Jesse Pajwani, Jose Felipe Voloch

For a variety over a global field, one can consider subsets of the set of adelic points of the variety cut out by finite abelian descent or Brauer-Manin obstructions. Given a Galoi…

math.NT2024

Etale descent obstruction and anabelian geometry of curves over finite fields

Brendan Creutz, Jose Felipe Voloch

Let $C$ and $D$ be smooth, proper and geometrically integral curves over a finite field $F$ . Any morphism from $D$ to $C$ induces a morphism of their étale fundamental groups. The…