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On abelian points of varieties intersecting subgroups in a torus

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Mello,  Jorge
Max Planck Institute for Mathematics, Max Planck Society;

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Mello, J. (2022). On abelian points of varieties intersecting subgroups in a torus. Journal de Théorie des Nombres de Bordeaux, 34(1), 309-322. doi:10.5802/jtnb.1203.


Cite as: https://hdl.handle.net/21.11116/0000-000A-DBCC-A
Abstract
We show, under some natural conditions, that the set of abelian points on the
non-anomalous subset of a closed irreducible subvariety $X$ intersected with
the union of connected algebraic subgroups of codimension at least $\dim X$ in
a torus is finite, generalising results of Ostafe, Sha, Shparlinski and Zannier
(2017). We also generalise their structure theorem for such sets when the
algebraic subgroups are not necessarily connected, and obtain a related result
in the context of curves and arithmetic dynamics.