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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie

IMPACT FACTOR 2018: 1.859

CiteScore 2018: 1.14

SCImago Journal Rank (SJR) 2018: 2.554
Source Normalized Impact per Paper (SNIP) 2018: 1.411

Mathematical Citation Quotient (MCQ) 2018: 1.55

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Volume 2015, Issue 705


Families of abelian varieties with many isogenous fibres

Martin Orr
Published Online: 2013-07-23 | DOI: https://doi.org/10.1515/crelle-2013-0058


Let Z be a subvariety of the moduli space of principally polarised abelian varieties of dimension g over the complex numbers. Suppose that Z contains a Zariski dense set of points which correspond to abelian varieties from a single isogeny class. A generalisation of a conjecture of André and Pink predicts that Z is a weakly special subvariety. We prove this when dimZ=1 using the Pila–Zannier method and the Masser–Wüstholz isogeny theorem. This generalises results of Edixhoven and Yafaev when the Hecke orbit consists of CM points and of Pink when it consists of Galois generic points.

About the article

Received: 2013-01-28

Revised: 2013-05-29

Published Online: 2013-07-23

Published in Print: 2015-08-01

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2015, Issue 705, Pages 211–231, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/crelle-2013-0058.

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