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pro vyhledávání: '"Gabriel, Andreas"'
Inspired by recent work of Aslanyan and Daw, we introduce the notion of $\Sigma$-orbits in the general framework of distinguished categories. In the setting of connected Shimura varieties, this concept contains many instances of (generalized) Hecke o
Externí odkaz:
http://arxiv.org/abs/2401.11193
We characterise the integral affine plane curves over a finite field $k$ with the property that all but finitely many of their $\overline{k}$-points have coordinates that are $j$-invariants of elliptic curves with isomorphic endomorphism rings. This
Externí odkaz:
http://arxiv.org/abs/2308.10976
Let $H_D(T)$ denote the Hilbert class polynomial of the imaginary quadratic order of discriminant $D$. We study the rate of growth of the greatest common divisor of $H_D(a)$ and $H_D(b)$ as $|D| \to \infty$ for $a$ and $b$ belonging to various Dedeki
Externí odkaz:
http://arxiv.org/abs/2204.13461
Autor:
Dill, Gabriel Andreas
Let $K$ be a field of characteristic $0$ and let $G$ and $H$ be connected commutative algebraic groups over $K$. Let $\text{Mor}_0(G,H)$ denote the set of morphisms of algebraic varieties $G \to H$ that map the neutral element to the neutral element.
Externí odkaz:
http://arxiv.org/abs/2107.14667
We propose an axiomatic approach towards studying unlikely intersections by introducing the framework of distinguished categories. This includes commutative algebraic groups and mixed Shimura varieties. It allows us to define all basic concepts of th
Externí odkaz:
http://arxiv.org/abs/2103.07422
Autor:
Dill, Gabriel Andreas
Publikováno v:
Research in Number Theory, 7, no. 33 (2021)
We count algebraic numbers of fixed degree $d$ and fixed (absolute multiplicative Weil) height $\mathcal{H}$ with precisely $k$ conjugates that lie inside the open unit disk. We also count the number of values up to $\mathcal{H}$ that the height assu
Externí odkaz:
http://arxiv.org/abs/2012.09085
Autor:
Dill, Gabriel Andreas
Publikováno v:
Compos. Math. 158 (2022), 1020-1051
Investigating a conjecture of Zannier, we study irreducible subvarieties of abelian schemes that dominate the base and contain a Zariski dense set of torsion points that lie on pairwise isogenous fibers. If everything is defined over the algebraic nu
Externí odkaz:
http://arxiv.org/abs/2011.05815
Autor:
Stüben, Björn-Ole1 (AUTHOR) rainer.schmeding@uk-essen.de, Plitzko, Gabriel Andreas2 (AUTHOR) gabriel@plitzko.net, Stern, Louisa2 (AUTHOR) l.stern@uke.de, Schmeding, Rainer1 (AUTHOR) juergen-walter.treckmann@uk-essen.de, Karstens, Karl-Frederick2 (AUTHOR) kf.karstens@gmail.com, Reeh, Matthias2 (AUTHOR) matthias.reeh@arcor.de, Treckmann, Jürgen Walter1 (AUTHOR) fuat.saner@me.com, Izbicki, Jakob Robert2 (AUTHOR) izbicki@uke.de, Saner, Fuat Hakan1 (AUTHOR) jan.neuhaus@uk-essen.de, Neuhaus, Jan Peter1 (AUTHOR) dieter.hoyer@uk-essen.de, Tachezy, Michael2 (AUTHOR) tachezym@gmail.com, Hoyer, Dieter Paul1 (AUTHOR)
Publikováno v:
Journal of Clinical Medicine. Feb2024, Vol. 13 Issue 4, p1137. 10p.
In this article, we prove that the Zilber-Pink conjecture for abelian varieties over an arbitrary field of characteristic $0$ is implied by the same statement for abelian varieties over the algebraic numbers. More precisely, the conjecture holds for
Externí odkaz:
http://arxiv.org/abs/1909.01271
Autor:
Dill, Gabriel Andreas
Publikováno v:
Mathematische Annalen, 377(3), 1509-1545 (2020)
Fix an elliptic curve $E_0$ without CM and a non-isotrivial elliptic scheme over a smooth irreducible curve, both defined over the algebraic numbers. Consider the union of all images of a fixed finite-rank subgroup (of arbitrary rank) of $E_0^g$, als
Externí odkaz:
http://arxiv.org/abs/1902.01323