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 subvarieties of dimension at most $m$ in the abelian variety $A$ if it holds for subvarieties of dimension at most $m$ in the largest abelian subvariety of $A$ that is isomorphic to an abelian variety defined over $ar{ mathbb{Q}}$.
Barroero, F., Dill, G. (2022). On the Zilber-Pink conjecture for complex abelian varieties. ANNALES SCIENTIFIQUES DE L'ECOLE NORMALE SUPERIEURE, 55(1), 261-282 [10.24033/asens.2496].
On the Zilber-Pink conjecture for complex abelian varieties
Fabrizio Barroero;
2022-01-01
Abstract
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 subvarieties of dimension at most $m$ in the abelian variety $A$ if it holds for subvarieties of dimension at most $m$ in the largest abelian subvariety of $A$ that is isomorphic to an abelian variety defined over $ar{ mathbb{Q}}$.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
