Zobrazeno 1 - 10
of 55
pro vyhledávání: '"Dittmann, Philip"'
Autor:
Daans, Nicolas, Dittmann, Philip
We establish that all rings of $S$-integers are universally definable in function fields in one variable over certain ground fields including global and non-archimedean local fields. That is, we show that the complement of such a ring of $S$-integers
Externí odkaz:
http://arxiv.org/abs/2404.02749
Autor:
Dittmann, Philip, Fehm, Arno
We discuss the common existential theory of all or almost all completions of a global function field.
Comment: minor changes to Introduction and Remark 6.2
Comment: minor changes to Introduction and Remark 6.2
Externí odkaz:
http://arxiv.org/abs/2401.11930
We study function fields of curves over a base field $K$ which is either a global field or a large field having a separable field extension of degree divisible by $4$. We show that, for any such function field, Hilbert's 10th Problem has a negative a
Externí odkaz:
http://arxiv.org/abs/2311.06044
Autor:
Dittmann, Philip
We show that each local field $\mathbb{F}_q((t))$ of characteristic $p > 0$ is characterised up to isomorphism within the class of all fields of imperfect exponent at most $1$ by (certain small quotients of) its absolute Galois group together with na
Externí odkaz:
http://arxiv.org/abs/2309.05398
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 the induced structure on the residue field and show that once the resid
Externí odkaz:
http://arxiv.org/abs/2305.12145
Autor:
Dittmann, Philip
We construct an existentially undecidable complete discretely valued field of mixed characteristic with existentially decidable residue field and decidable algebraic part, answering a question by Anscombe-Fehm in a strong way. Along the way, we const
Externí odkaz:
http://arxiv.org/abs/2211.01775
We investigate the following question: Given a field $K$, when is the \'etale open topology $\mathcal{E}_K$ induced by a field topology? On the positive side, when $K$ is the fraction field of a local domain $R\neq K$, using a weak form of resolution
Externí odkaz:
http://arxiv.org/abs/2208.02398
Publikováno v:
Model Th. 2 (2023) 101-120
We study the definability of convex valuations on ordered fields, with a particular focus on the distinguished subclass of henselian valuations. In the setting of ordered fields, one can consider definability both in the language of rings $\mathcal{L
Externí odkaz:
http://arxiv.org/abs/2206.15301
Publikováno v:
Alg. Number Th. 17 (2023) 2013-2032
We study the existential theory of equicharacteristic henselian valued fields with a distinguished uniformizer. In particular, assuming a weak consequence of resolution of singularities, we obtain an axiomatization of - and therefore an algorithm to
Externí odkaz:
http://arxiv.org/abs/2205.05438
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 associated to such a definition.
Comment: Expanded results in Secti
Comment: Expanded results in Secti
Externí odkaz:
http://arxiv.org/abs/2102.06941