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pro vyhledávání: '"Kartas, Konstantinos"'
Autor:
Kartas, Konstantinos
A field $k$ is called geometrically $C_1$ if every smooth projective separably rationally connected $k$-variety has a $k$-rational point. Given a henselian valued field of equal characteristic $0$ with divisible value group, we show that the property
Externí odkaz:
http://arxiv.org/abs/2407.19986
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 extension of the tilt. This specializes to the almost purity theorem over pe
Externí odkaz:
http://arxiv.org/abs/2304.05881
Autor:
Kartas, Konstantinos
When $k$ is a finite field, Becker-Denef-Lipschitz (1979) observed that the total residue map $\text{res}:k(\!(t)\!)\to k$, which picks out the constant term of the Laurent series, is definable in the language of rings with a parameter for $t$. Drive
Externí odkaz:
http://arxiv.org/abs/2203.02374
Autor:
Kartas, Konstantinos
Publikováno v:
Annals of Pure and Applied Logic, Volume 174, Issue 2, February 2023
Fix a prime $p$. We prove that the set of sentences true in all but finitely many finite extensions of $\mathbb{Q}_p$ is undecidable in the language of valued fields with a cross-section. The proof goes via reduction to characteristic $p$, adapting P
Externí odkaz:
http://arxiv.org/abs/2105.03771
Autor:
Kartas, Konstantinos
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 specializes to well-known results in residue characteristic $0$ and unramified m
Externí odkaz:
http://arxiv.org/abs/2103.14646
Autor:
Kartas, Konstantinos
Publikováno v:
Algebra & Number Theory, Volume 18 2024 No. 2
We prove a relative decidability result for perfectoid fields. This applies to show that the fields $\mathbb{Q}_p(p^{1/p^{\infty}})$ and $\mathbb{Q}_p(\zeta_{p^{\infty}})$ are (existentially) decidable relative to the perfect hull of $ \mathbb{F}_p(\
Externí odkaz:
http://arxiv.org/abs/2001.04424
Autor:
Kartas, Konstantinos
Publikováno v:
Journal of Mathematical Logic; Dec2024, Vol. 24 Issue 3, p1-14, 14p
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