5 citations · 8 across the 8 of their papers we have counts for
8 papers
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…
Perfectoid transfer
Konstantinos Kartas
We prove a perfectoid analogue of the Ax-Kochen theorem on zeros of -adic forms: Given , there is a finite totally ramified extension such that…
On geometrically fields
Konstantinos Kartas
A field is called geometrically if every smooth projective separably rationally connected -variety has a -rational point. Given a henselian valued field of equal ch…
Beyond the Fontaine-Wintenberger theorem
Franziska Jahnke, Konstantinos Kartas
Given a perfectoid field, we find an elementary extension and a henselian defectless valuation on it, whose value group is divisible and whose residue field is an elementary extens…
Valued fields with a total residue map
Konstantinos Kartas
When is a finite field, Becker-Denef-Lipschitz (1979) observed that the total residue map , which picks out the constant term of the Laurent series,…
An undecidability result for the asymptotic theory of -adic fields
Konstantinos Kartas
Fix a prime . We prove that the set of sentences true in all but finitely many finite extensions of is undecidable in the language of valued fields with a cross-s…
Diophantine problems over tamely ramified fields
Konstantinos Kartas
Assuming a certain form of resolution of singularities, we prove a general existential Ax-Kochen/Ershov principle for tamely ramified fields in all characteristics. This specialize…
Decidability via the tilting correspondence
Konstantinos Kartas
We prove a relative decidability result for perfectoid fields. This applies to show that the fields and are (existen…