3 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.NT2020
Hereditarily non-pythagorean fields
David Grimm, David B. Leep
We prove for a large class of fields that every proper finite extension of , the pythagorean closure of , is not a pythagorean field. This class of fields contains…
math.OC2006
A note on the representation of positive polynomials with structured sparsity
David Grimm, Tim Netzer, Markus Schweighofer
We consider real polynomials in finitely many variables. Let the variables consist of finitely many blocks that are allowed to overlap in a certain way. Let the solution set of a f…