Level structures on Abelian varieties, Kodaira dimensions, and Lang's conjecture

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dc.citation.firstpage523
dc.citation.journalTitleAdvances in Mathematics
dc.citation.lastpage540
dc.citation.volumeNumber329
dc.contributor.authorAbramovich, Dan
dc.contributor.authorVárilly-Alvarado, Anthony
dc.date.accessioned2018-06-28T20:50:03Z
dc.date.available2018-06-28T20:50:03Z
dc.date.issued2018
dc.description.abstractAssuming Lang's conjecture, we prove that for a prime p, number field K, and positive integer g, there is an integer r such that no principally polarized abelian variety A/K has full level-pr structure. To this end, we use a result of Zuo to prove that for each closed subvariety X in the moduli space Ag of principally polarized abelian varieties of dimension g, there exists a level mX such that the irreducible components of the preimage of X in Ag[m] are of general type for m>mX.
dc.identifier.citationAbramovich, Dan and Várilly-Alvarado, Anthony. "Level structures on Abelian varieties, Kodaira dimensions, and Lang's conjecture." <i>Advances in Mathematics,</i> 329, (2018) Elsevier: 523-540. https://doi.org/10.1016/j.aim.2017.12.023.
dc.identifier.doihttps://doi.org/10.1016/j.aim.2017.12.023
dc.identifier.urihttps://hdl.handle.net/1911/102314
dc.language.isoeng
dc.publisherElsevier
dc.rightsThis is an author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by Elsevier.
dc.subject.keywordAbelian varieties
dc.subject.keywordModuli spaces
dc.subject.keywordBirational geometry
dc.subject.keywordRational points
dc.titleLevel structures on Abelian varieties, Kodaira dimensions, and Lang's conjecture
dc.typeJournal article
dc.type.dcmiText
dc.type.publicationpost-print
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