Zobrazeno 1 - 10
of 182
pro vyhledávání: '"12F20"'
Autor:
Massarenti, Alex
We show that even dimensional Fermat cubic hypersurfaces are rational over any field of characteristic different from three by producing explicit rational parametrizations given by polynomials of low degree. As a byproduct of our rationality construc
Externí odkaz:
http://arxiv.org/abs/2406.07223
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
Let $k$ be a field, $T$ be an algebraic $k$-torus, $X$ be a smooth $k$-compactification of $T$ and ${\rm Pic}\,\overline{X}$ be the Picard group of $\overline{X}=X\times_k\overline{k}$ where $\overline{k}$ is a fixed separable closure of $k$. Hoshi,
Externí odkaz:
http://arxiv.org/abs/2404.01362
Autor:
Chipchakov, Ivan D.
This paper considers K\"{o}the's question of whether every associative locally finite-dimensional (abbr., LFD) central division algebra $R$ over a field $K$ is a normally locally finite (abbr., NLF) algebra over $K$, that is, whether every nonempty f
Externí odkaz:
http://arxiv.org/abs/2403.14564
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:
Hoshi, Akinari, Yamasaki, Aiichi
We give a complete answer to the rationality problem (up to stable $k$-equivalence) for norm one tori $T=R^{(1)}_{K/k}(\mathbb{G}_m)$ of $K/k$ whose Galois closures $L/k$ are $A_5\simeq {\rm PSL}_2(\mathbb{F}_4)$ and ${\rm PSL}_2(\mathbb{F}_8)$ exten
Externí odkaz:
http://arxiv.org/abs/2309.16187
Autor:
Grabowski, Przemyslaw
We prove a Galois-type correspondence between compositions of purely inseparable field extensions (including infinite ones) and subalgebras of differential operators. This correspondence can be utilized to establish a connection between separable fie
Externí odkaz:
http://arxiv.org/abs/2307.11746
Autor:
Hou, Xiang-dong
Two rational functions $f,g\in\Bbb F_q(X)$ are said to be {\em equivalent} if there exist $\phi,\psi\in\Bbb F_q(X)$ of degree one such that $g=\phi\circ f\circ\psi$. We give an explicit formula for the number of equivalence classes of rational functi
Externí odkaz:
http://arxiv.org/abs/2305.20008
Publikováno v:
Journal of Pure and Applied Algebra, Volume 228. Issue 3, March 2024, 107492
It is shown that a valuation of residue characteristic different from $2$ and $3$ on a field $E$ has at most one extension to the function field of an elliptic curve over $E$, for which the residue field extension is transcendental but not ruled. The
Externí odkaz:
http://arxiv.org/abs/2303.02100
Autor:
Hoshi, Akinari, Yamasaki, Aiichi
We give a complete answer to the rationality problem (up to stable $k$-equivalence) for norm one tori $R^{(1)}_{K/k}(\mathbb{G}_m)$ of $K/k$ whose Galois closures $L/k$ are dihedral extensions with the aid of Endo and Miyata [EM75, Theorem 1.5, Theor
Externí odkaz:
http://arxiv.org/abs/2302.06231