Zobrazeno 1 - 10
of 135
pro vyhledávání: '"Petersen, Sebastian"'
Autor:
Gajda, Wojciech, Petersen, Sebastian
Let $A$ be an abelian variety defined over a field $K.$ We study finite generation properties of the profinite group $\mathrm{Gal}(\Omega/K)$ and of certain closed normal subgroups thereof, where $\Omega$ is the torsion field of $A$ over $K$. In fact
Externí odkaz:
http://arxiv.org/abs/2401.05805
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
Autor:
Gajda, Wojciech, Petersen, Sebastian
Let $A$ and $B$ be abelian varieties defined over the function field $k(S)$ of a smooth algebraic variety $S/k.$ We establish criteria, in terms of restriction maps to subvarieties of $S,$ for existence of various important classes of $k(S)$-homomorp
Externí odkaz:
http://arxiv.org/abs/2207.09345
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:
Fehm, Arno, Petersen, Sebastian
Let $A$ be a non-zero abelian variety over a field $F$ that is not algebraic over a finite field. We prove that the rational rank of the abelian group $A(F)$ is infinite when $F$ is large in the sense of Pop (also called ample). The main ingredient i
Externí odkaz:
http://arxiv.org/abs/1912.10710
Publikováno v:
In Finance Research Letters July 2023 55 Part A
Let $X$ be a normal geometrically connected variety over a finite field $\kappa$ of characteristic~$p$. Let $E$ be a number field. Using automorphic methods over global function fields, we derive properties of the geometric monodromy groups of arbitr
Externí odkaz:
http://arxiv.org/abs/1901.03654
In this note we prove a variational open adelic image theorem for the Galois action on the cohomology of smooth proper $S$-schemes where $S$ is a smooth variety over a finitely generated field of positive characteristic. A central tool is a recent re
Externí odkaz:
http://arxiv.org/abs/1701.04747
Autor:
Petersen, Sebastian
Publikováno v:
Acta Arithmetica 176.2 (2016), p. 161--176
Let $K/\mathbb{Q}$ be a finitely generated field of characteristic zero and $X/K$ a smooth projective variety. Fix $q\in\mathbb{N}$. For every prime number $\ell$ let $\rho_\ell$ be the representation of $\mathrm{Gal}(K)$ on the \'etale cohomology gr
Externí odkaz:
http://arxiv.org/abs/1701.04757