Unlikely intersections with isogeny orbits in a product of elliptic schemes

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Authors

  • Gabriel A. Dill

External Research Organisations

  • University of Basel
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Details

Original languageEnglish
Pages (from-to)1509–1545
Number of pages37
JournalMathematische Annalen
Volume377
Issue number3-4
Early online date17 Jun 2020
Publication statusPublished - Aug 2020
Externally publishedYes

Abstract

Fix an elliptic curve E without CM and a non-isotrivial elliptic scheme over a smooth irreducible curve, both defined over the algebraic numbers. Consider the union of all images of a fixed finite-rank subgroup (of arbitrary rank) of E0g, also defined over the algebraic numbers, under all isogenies between E0g and some fiber of the g-th fibered power A of the elliptic scheme, where g is a fixed natural number. As a special case of a slightly more general result, we characterize the subvarieties (of arbitrary dimension) inside A that have potentially Zariski dense intersection with this set. In the proof, we combine a generalized Vojta–Rémond inequality with the Pila–Zannier strategy.

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Cite this

Unlikely intersections with isogeny orbits in a product of elliptic schemes. / Dill, Gabriel A.
In: Mathematische Annalen, Vol. 377, No. 3-4, 08.2020, p. 1509–1545.

Research output: Contribution to journalArticleResearchpeer review

Dill GA. Unlikely intersections with isogeny orbits in a product of elliptic schemes. Mathematische Annalen. 2020 Aug;377(3-4):1509–1545. Epub 2020 Jun 17. doi: 10.1007/s00208-020-02024-2
Dill, Gabriel A. / Unlikely intersections with isogeny orbits in a product of elliptic schemes. In: Mathematische Annalen. 2020 ; Vol. 377, No. 3-4. pp. 1509–1545.
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