Zobrazeno 1 - 10
of 366
pro vyhledávání: '"12E25"'
Autor:
Seguin, Béranger
Let $K$ be a field of characteristic $0$ and $k \geq 2$ be an integer. We prove that every $K$-linear bijection $f : K[X] \to K[X]$ strongly preserving the set of $k$-free polynomials (or the set of polynomials with a $k$-fold root in $K$) is a const
Externí odkaz:
http://arxiv.org/abs/2407.09118
Let $f(t_1, \ldots, t_r, X)\in \mathbb{Z}[t_1, \ldots, t_r,X]$ be irreducible and let $a_1, \ldots, a_r\in \mathbb{Z} \smallsetminus \{0,\pm 1\}$. Under a necessary ramification assumption on $f$, and conditionally on the Generalized Riemann Hypothes
Externí odkaz:
http://arxiv.org/abs/2405.04058
We study the preservation of the Hilbert property and of the weak Hilbert property under base change in field extensions. In particular we show that these properties are preserved if the extension is finitely generated or Galois with finitely generat
Externí odkaz:
http://arxiv.org/abs/2312.16219
We study rational points on ramified covers of abelian varieties over certain infinite Galois extensions of $\mathbb{Q}$. In particular, we prove that every elliptic curve $E$ over $\mathbb{Q}$ has the weak Hilbert property of Corvaja-Zannier both ov
Externí odkaz:
http://arxiv.org/abs/2206.01582
Autor:
Kaltofen, Erich L.
Let f(x) = x^n + (a[n-1] t + b[n-1]) x^(n-1) + ... + (a[0] t + b[0]) be of constant degree n in x and degree <= 1 in t, where all a[i],b[i] are randomly and uniformly selected from a finite field GF(q) of q elements. Then the probability that the Gal
Externí odkaz:
http://arxiv.org/abs/2204.02836
Autor:
Paredes, Marcelo, Sasyk, Román
We prove an effective form of Hilbert's irreducibility theorem for polynomials over a global field $K$. More precisely, we give effective bounds for the number of specializations $t\in \mathcal{O}_K$ that do not preserve the irreducibility or the Gal
Externí odkaz:
http://arxiv.org/abs/2202.10420
Autor:
Bary-Soroker, Lior, Garzoni, Daniele
Let $G$ be a connected linear algebraic group over a number field $K$, let $\Gamma$ be a finitely generated Zariski dense subgroup of $G(K)$ and let $Z\subseteq G(K)$ be a thin set, in the sense of Serre. We prove that, if $G/\mathrm{R}_u(G)$ is semi
Externí odkaz:
http://arxiv.org/abs/2202.05010
Autor:
Iadarola, Angelo
Hilbert specialization is an important tool in Field Arithmetic and Arithmetic Geometry, which has usually been intended for polynomials, hence hypersurfaces, and at scalar values. In this article, first, we extend this tool to prime ideals, hence af
Externí odkaz:
http://arxiv.org/abs/2104.05455
Autor:
Dittmann, Philip, Kadets, Borys
Publikováno v:
Proc. Amer. Math. Soc. 150 (2022), 3335-3343
Suppose $f \in K[x]$ is a polynomial. The absolute Galois group of $K$ acts on the preimage tree $\mathrm{T}$ of $0$ under $f$. The resulting homomorphism $\phi_f: \mathrm{Gal}_K \to \mathrm{Aut} \mathrm{T}$ is called the arboreal Galois representati
Externí odkaz:
http://arxiv.org/abs/2012.03076
Autor:
Monderer, Tali, Neftin, Danny
Given an irreducible bivariate polynomial $f(t,x)\in \mathbb{Q}[t,x]$, what groups $H$ appear as the Galois group of $f(t_0,x)$ for infinitely many $t_0\in \mathbb{Q}$? How often does a group $H$ as above appear as the Galois group of $f(t_0,x)$, $t_
Externí odkaz:
http://arxiv.org/abs/2003.11324