2 papers
math.NT2025
Arithmetic genus inequalities with an application to sums of squares
David Grimm, Gonzalo Manzano-Flores
We show variants of the genus inequality for the irreducible components of the special fiber of an arithmetic curve over a henselian discrete valuation ring of residue characterist…
math.NT2024
The Pythagoras number of a rational function field in two variables
Karim Johannes Becher, Nicolas Daans, David Grimm +2
We prove that every sum of squares in the rational function field in two variables over a hereditarily pythagorean field is a sum of squares. More precisely, we sh…