Published by Duke University Press since its inception in 1935, the Duke Mathematical Journal is one of the world's leading mathematical journals. DMJ emphasizes the most active and influential areas of current mathematics. Advance publication of articles online is available.

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  • ISSN: 0012-7094 (print), 1547-7398 (electronic)
  • Publisher: Duke University Press
  • Discipline(s): Mathematics
  • Full text available in Euclid: 1935--
  • Access: By subscription only
  • Euclid URL:

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MR Citation Database MCQ (2016): 2.23
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Eigenfactor: Duke Mathematical Journal
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Featured article

Bounded height in pencils of finitely generated subgroups

F. Amoroso , D. Masser , and U. Zannier Volume 166, Number 13 (2017)

In this article we prove a general bounded height result for specializations in finitely generated subgroups varying in families which complements and sharpens the toric Mordell–Lang theorem by replacing finiteness with emptiness, for the intersection of varieties and subgroups, all moving in a pencil, except for bounded height values of the parameters (and excluding identical relations). More precisely, an instance of the result is as follows. Consider the torus scheme Gmr/C over a curve C defined over Q¯, and let Γ be a subgroup scheme generated by finitely many sections (satisfying some necessary conditions). Further, let V be any subscheme. Then there is a bound for the height of the points PC(Q¯) such that, for some γΓ which does not generically lie in V, γ(P) lies in the fiber VP. We further offer some direct Diophantine applications, to illustrate once again that the results implicitly contain information absent from the previous bounds in this context.