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dc.contributor.authorUlmer, Douglas
dc.date.accessioned2019-09-06T04:31:28Z
dc.date.available2019-09-06T04:31:28Z
dc.date.issued2019-07-12
dc.identifier.citationUlmer, D. (2019). On the Brauer–Siegel ratio for abelian varieties over function fields. Algebra & Number Theory, 13(5), 1069-1120.en_US
dc.identifier.issn1937-0652
dc.identifier.doi10.2140/ant.2019.13.1069
dc.identifier.urihttp://hdl.handle.net/10150/634120
dc.description.abstractHindry has proposed an analog of the classical Brauer–Siegel theorem for abelian varieties over global fields. Roughly speaking, it says that the product of the regulator of the Mordell–Weil group and the order of the Tate–Shafarevich group should have size comparable to the exponential differential height. Hindry–Pacheco and Griffon have proved this for certain families of elliptic curves over function fields using analytic techniques. Our goal in this work is to prove similar results by more algebraic arguments, namely by a direct approach to the Tate–Shafarevich group and the regulator. We recover the results of Hindry–Pacheco and Griffon and extend them to new families, including families of higher-dimensional abelian varieties.en_US
dc.language.isoenen_US
dc.publisherMATHEMATICAL SCIENCE PUBLen_US
dc.rightsCopyright © 2019 Mathematical Sciences Publishers; first published in Algebra & Number Theory in Vol. 13 (2019), No. 5, published by Mathematical Sciences Publishers.en_US
dc.subjectabelian varietyen_US
dc.subjectTate-Shafarevich groupen_US
dc.subjectregulatoren_US
dc.subjectheighten_US
dc.subjectBrauer-Siegel ratioen_US
dc.subjectfunction fielden_US
dc.titleOn the Brauer–Siegel ratio for abelian varieties over function fieldsen_US
dc.typeArticleen_US
dc.contributor.departmentUniv Arizona, Dept Mathen_US
dc.identifier.journalALGEBRA & NUMBER THEORYen_US
dc.description.collectioninformationThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu.en_US
dc.eprint.versionFinal published versionen_US
dc.source.volume13
dc.source.issue5
dc.source.beginpage1069-1120
refterms.dateFOA2019-09-06T04:31:29Z


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