5 papers
Ax-Kochen-Ershov principles for finitely ramified henselian fields
Sylvy Anscombe, Philip Dittmann, Franziska Jahnke
We study the model theory of finitely ramified henselian valued fields of fixed initial ramification, obtaining versions of the Ax-Kochen-Ershov principle as follows. We identify t…
On the existential theory of the completions of a global field
Philip Dittmann, Arno Fehm
We discuss the common existential theory of all or almost all completions of a global function field.
Existential rank and essential dimension of diophantine sets
Nicolas Daans, Philip Dittmann, Arno Fehm
We study the minimal number of existential quantifiers needed to define a diophantine set over a field and relate this number to the essential dimension of the functor of points as…
Uniform existential definitions of valuations in function fields in one variable
Karim Johannes Becher, Nicolas Daans, Philip Dittmann
We study function fields of curves over a base field which is either a global field or a large field having a separable field extension of degree divisible by . We show that…
When is the étale open topology a field topology?
Philip Dittmann, Erik Walsberg, Jinhe Ye
We investigate the following question: Given a field , when is the étale open topology induced by a field topology? On the positive side, when is the fracti…