Nicolas Daans

collaborators

5 papers

math.NT2025

Existentially defining valuations in function fields over large fields

Nicolas Daans

Let $K$ be a large field such that $K [- 1]$ is not algebraically closed and $F / K$ a function field in one variable. Extending techniques and results from earlier work with Be…

math.NT2025

Decidability of polynomial equations over function fields in positive characteristic

Nicolas Daans

Let $K$ be a field of positive characteristic with no algebraically closed subfield. Let $F$ be a function field over $K$ and $t \in F$ transcendental over $K$ . Refining a result o…

math.NT2025

The u-invariant of function fields in one variable

Karim Johannes Becher, Nicolas Daans, Vlerë Mehmeti

The u-invariant of a field is the largest dimension of an anisotropic quadratic torsion form over the field. In this article we obtain a bound on the u-invariant of function fields…

math.NT2025

Pythagoras numbers for infinite algebraic fields

Nicolas Daans, Stevan Gajović, Siu Hang Man +1

We prove that the Pythagoras number of the ring of integers of the compositum of all real quadratic fields is infinite. The same holds for certain infinite totally real cyclotomic…

math.NT2024

Most totally real fields do not have universal forms or Northcott property

Nicolas Daans, Vitezslav Kala, Siu Hang Man +2

We show that, in the space of all totally real fields equipped with the constructible topology, the set of fields that admit a universal quadratic form, or have the Northcott prope…