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of 324
pro vyhledávání: '"Ghioca, Dragos"'
In [GTZ08, GTZ12], the following result was established: given polynomials $f,g\in\mathbb{C}[x]$ of degrees larger than $1$, if there exist $\alpha,\beta\in\mathbb{C}$ such that their corresponding orbits $\mathcal{O}_f(\alpha)$ and $\mathcal{O}_g(\b
Externí odkaz:
http://arxiv.org/abs/2408.06937
Autor:
Asgarli, Shamil, Ghioca, Dragos
We examine the maximum dimension of a linear system of plane cubic curves whose $\mathbb{F}_q$-members are all geometrically irreducible. Computational evidence suggests that such a system has a maximum (projective) dimension of $3$. As a step toward
Externí odkaz:
http://arxiv.org/abs/2407.18104
Autor:
Ghioca, Dragos
In the goundbreaking paper [BD11] (which opened a wide avenue of research regarding unlikely intersections in arithmetic dynamics), Baker and DeMarco prove that for the family of polynomials $f_\lambda(x):=x^d+\lambda$ (parameterized by $\lambda\in\m
Externí odkaz:
http://arxiv.org/abs/2402.16179
Let $d$ and $n$ be positive integers, and $E/F$ be a separable field extension of degree $m=\binom{n+d}{n}$. We show that if $|F| > 2$, then there exists a point $P\in \mathbb{P}^n(E)$ which does not lie on any degree $d$ hypersurface defined over $F
Externí odkaz:
http://arxiv.org/abs/2310.10361
We obtain a criterion for when the specialization of the iterated Galois group for a post-critically finite (PCF) rational map is as large as possible, i.e., it equals the generic iterated Galois group for the given map.
Externí odkaz:
http://arxiv.org/abs/2309.00840
Autor:
Asgarli, Shamil, Ghioca, Dragos
A plane curve $C$ in $\mathbb{P}^2$ defined over $\mathbb{F}_q$ is called plane-filling if $C$ contains every $\mathbb{F}_q$-point of $\mathbb{P}^2$. Homma and Kim, building on the work of Tallini, proved that the minimum degree of a smooth plane-fil
Externí odkaz:
http://arxiv.org/abs/2307.03072
The Mordell-Lang conjecture for semiabelian varieties defined over fields of positive characteristic
Autor:
Ghioca, Dragos, Yang, She
Let $G$ be a semiabelian variety defined over an algebraically closed field $K$ of prime characteristic. We describe the intersection of a subvariety $X$ of $G$ with a finitely generated subgroup of $G(K)$.
Comment: 10 pages
Comment: 10 pages
Externí odkaz:
http://arxiv.org/abs/2306.03420
Autor:
Coccia, Simone, Ghioca, Dragos
Publikováno v:
Journal of Number Theory 216 (2020) 142-156
We complete the proof of a Siegel type statement for finitely generated $\Phi$-submodules of $\mathbb{G}_a$ under the action of a Drinfeld module $\Phi$.
Comment: 14 pages. arXiv admin note: text overlap with arXiv:0704.1331
Comment: 14 pages. arXiv admin note: text overlap with arXiv:0704.1331
Externí odkaz:
http://arxiv.org/abs/2303.00118
Autor:
Asgarli, Shamil, Ghioca, Dragos
We study plane curves over finite fields whose tangent lines at smooth $\mathbb{F}_q$-points together cover all the points of $\mathbb{P}^2(\mathbb{F}_q)$.
Comment: 13 pages
Comment: 13 pages
Externí odkaz:
http://arxiv.org/abs/2302.13420
Publikováno v:
Finite Fields Appl. 92 (2023), Paper No. 102283, 11 pp
We prove that there is a pencil of hypersurfaces in $\mathbb{P}^n$ of any given degree over a finite field $\mathbb{F}_q$ such that every $\mathbb{F}_q$-member of the pencil is not blocking with respect to $\mathbb{F}_q$-lines.
Comment: 8 pages
Comment: 8 pages
Externí odkaz:
http://arxiv.org/abs/2301.09215