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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…