1 citations · 2 across the 4 of their papers we have counts for
5 papers
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…
Sums of squares in function fields over a henselian valued field
Karim Johannes Becher, Nicolas Daans, David Grimm +2
The Pythagoras number of a field is the smallest natural number such that every sum of squares in the field is a sum of squares. Given a nondyadic henselian valued field $(…
Nonsplit conics in the reduction of an arithmetic curve
Karim Johannes Becher, David Grimm
For an algebraic function field and a discrete valuation of with perfect residue field , we bound the number of discrete valuations on extending whose resi…
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…
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…