1 citations · 2 across the 4 of their papers we have counts for
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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…