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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

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1435-5345
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Volume 2018, Issue 741

Issues

Trace of abelian varieties over function fields and the geometric Bogomolov conjecture

Kazuhiko Yamaki
Published Online: 2016-01-27 | DOI: https://doi.org/10.1515/crelle-2015-0086

Abstract

We prove that the geometric Bogomolov conjecture for any abelian varieties is reduced to that for nowhere degenerate abelian varieties with trivial trace. In particular, the geometric Bogomolov conjecture holds for abelian varieties whose maximal nowhere degenerate abelian subvariety is isogenous to a constant abelian variety. To prove the results, we investigate closed subvarieties of abelian schemes over constant varieties, where constant varieties are varieties over a function field which can be defined over the constant field of the function field.

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About the article

Received: 2014-05-10

Revised: 2015-05-08

Published Online: 2016-01-27

Published in Print: 2018-08-01


Funding Source: Japan Society for the Promotion of Science

Award identifier / Grant number: KAKENHI 21740012

Award identifier / Grant number: KAKENHI 26800012

This work was partly supported by the Japan Society for the Promotion of Science through KAKENHI 21740012 and KAKENHI 26800012.


Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2018, Issue 741, Pages 133–159, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/crelle-2015-0086.

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