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Abelian varieties over finite fields as basic abelian varieties [PDF]

Forum Mathematicum, 2016
In this note we show that any basic abelian variety with additional structures over an arbitrary algebraically closed field of characteristic $p>0$ is isogenous to another one defined over a finite field.
Yu, Chia-Fu
core   +4 more sources

Non-isomorphic abelian varieties with the same arithmetic [PDF]

Royal Society Open Science
We construct two abelian varieties over [Formula: see text] which are not isomorphic, but have isomorphic Mordell–Weil groups over every number field, isomorphic Tate modules and equal values for several other invariants.
Jamie Bell
doaj   +2 more sources

Pseudo-abelian varieties [PDF]

Annales scientifiques de l'École normale supérieure, 2013
Chevalley's theorem states that every smooth connected algebraic group over a perfect field is an extension of an abelian variety by a smooth connected affine group. That fails when the base field is not perfect.
Totaro, Burt
core   +4 more sources

On the minimal model program for projective varieties with pseudo-effective tangent sheaf [PDF]

Épijournal de Géométrie Algébrique, 2023
In this paper, we develop a theory of pseudo-effective sheaves on normal projective varieties. As an application, by running the minimal model program, we show that projective klt varieties with pseudo-effective tangent sheaf can be decomposed into Fano ...
Shin-ichi Matsumura
doaj   +1 more source

Angehrn-Siu-Helmke’s method applied to abelian varieties

Forum of Mathematics, Sigma, 2023
We apply Angehrn-Siu-Helmke’s method to estimate basepoint freeness thresholds of higher dimensional polarized abelian varieties. We showed that a conjecture of Caucci holds for very general polarized abelian varieties in the moduli spaces $\mathcal {
Zhi Jiang
doaj   +1 more source

Non-linear bi-algebraic curves and surfaces in moduli spaces of Abelian differentials

Comptes Rendus. Mathématique, 2023
The strata of the moduli spaces of Abelian differentials are non-homogenous spaces carrying natural bi-algebraic structures. Partly inspired by the case of homogenous spaces carrying bi-algebraic structures (such as torii, Abelian varieties and Shimura ...
Deroin, Bertrand, Matheus, Carlos
doaj   +1 more source

Abelian varieties with isogenous reductions

Comptes Rendus. Mathématique, 2021
Let $A_1$ and $A_2$ be abelian varieties over a number field $K$. We prove that if there exists a non-trivial morphism of abelian varieties between reductions of $A_1$ and $A_2$ at a sufficiently high percentage of primes, then there exists a non-trivial
Khare, Chandrashekhar B., Larsen, Michael   +1 more
doaj   +1 more source

Free dihedral actions on abelian varieties

Cubo, 2021
We give a simple construction for hyperelliptic varieties, defined as the quotient of a complex torus by the action of a finite group $G$ that contains no translations and acts freely, with $G$ any dihedral group. This generalizes a construction given by
Bruno Aguiló Vidal
doaj   +1 more source

Compact connected components in relative character varieties of punctured spheres [PDF]

Épijournal de Géométrie Algébrique, 2021
We prove that some relative character varieties of the fundamental group of a punctured sphere into the Hermitian Lie groups $\mathrm{SU}(p,q)$ admit compact connected components.
Nicolas Tholozan, Jérémy Toulisse
doaj   +1 more source

Les strates ne possèdent pas de variétés complètes

Comptes Rendus. Mathématique, 2020
This note gives an elementary proof that the strata of abelian differentials do not contain complete algebraic varieties.
Gendron, Quentin
doaj   +1 more source