4 papers · 1 filter
Iterated toric descent obstruction and homogeneous spaces over geometric global fields
Felipe Gambardella, Nguyen Manh Linh
We study torsors under tori and groups of multiplicative type together with the obstruction they define to the existence of rational points in the setting of geometric global field…
Transfer principles and the Kato-Kuzumaki conjecture
Felipe Gambardella, Konstantinos Kartas
We show that for tame valued fields of equal characteristic with divisible value group, the property lifts from the residue field to the valued field under suitable hypothese…
Stability of the Kato-Kuzumaki's properties under field extensions
Felipe Gambardella, Harry C. Shaw
In 1986, Kato and Kuzumaki introduced some Diophantine properties of fields, called the properties, and they hoped they would provide a good characterization of the cohomol…
Reocurrence and weak approximation over geometric global fields
Felipe Gambardella
In this article, we prove a Reocurrence Theorem over function fields of curves over and over finite extensions of the Laurent series field $\mathbf{C}(\! (x…