The Betti map associated to a section of an abelian scheme

DOI10.1007/s00222-020-00963-wzbMath1460.11083arXiv1802.03204OpenAlexW3011522161WikidataQ104535813 ScholiaQ104535813MaRDI QIDQ2006708

Umberto Zannier, Yves André, Pietro Corvaja

Publication date: 12 October 2020

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1802.03204

zbMATH Keywords

torsionabelian varietiesKodaira-Spencer mapAx-Schanuel theoremBetti coordinatesManin theorem of kernel

Mathematics Subject Classification ID

Abelian varieties of dimension (> 1) (11G10) Special varieties (14M99) Algebraic moduli of abelian varieties, classification (14K10) Transcendence theory of elliptic and abelian functions (11J89)

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Betti maps, Pell equations in polynomials and almost-Belyi maps ⋮ The geometric Bogomolov conjecture ⋮ Uniformity in Mordell-Lang for curves ⋮ The relative Bogomolov conjecture for fibered products of elliptic curves ⋮ On the \(p\)-adic distribution of torsion values for a section of an abelian scheme ⋮ The number of rational points on a curve of genus at least two ⋮ The Ax-Schanuel conjecture for variations of mixed Hodge structures ⋮ Greatest common divisor results on semiabelian varieties and a conjecture of Silverman ⋮ Diophantine approximations. Abstracts from the workshop held April 17--23, 2022 ⋮ Finiteness theorems on elliptical billiards and a variant of the dynamical Mordell–Lang conjecture ⋮ Pfaffian definitions of Weierstrass elliptic functions ⋮ Mixed Ax–Schanuel for the universal abelian varieties and some applications ⋮ Generic rank of Betti map and unlikely intersections ⋮ Unramified sections of the Legendre scheme and modular forms ⋮ On the torsion values for sections of an elliptic scheme

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