Details
| Original language | English |
|---|---|
| Pages (from-to) | 261-282 |
| Number of pages | 22 |
| Journal | Annales Scientifiques de l'Ecole Normale Superieure |
| Volume | 55 |
| Issue number | 1 |
| Publication status | Published - 1 Jan 2022 |
| Externally published | Yes |
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 field of 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 Q N.
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
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In: Annales Scientifiques de l'Ecole Normale Superieure, Vol. 55, No. 1, 01.01.2022, p. 261-282.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On the Zilber-Pink conjecture for complex abelian varieties
AU - Barroero, Fabrizio
AU - Dill, Gabriel A.
N1 - Publisher Copyright: © 2022 Société Mathématique de France.
PY - 2022/1/1
Y1 - 2022/1/1
N2 - 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 field of 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 Q N.
AB - 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 field of 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 Q N.
UR - http://www.scopus.com/inward/record.url?scp=85171538519&partnerID=8YFLogxK
U2 - 10.24033/asens.2496
DO - 10.24033/asens.2496
M3 - Article
VL - 55
SP - 261
EP - 282
JO - Annales Scientifiques de l'Ecole Normale Superieure
JF - Annales Scientifiques de l'Ecole Normale Superieure
SN - 0012-9593
IS - 1
ER -