@prefix vivo: . @prefix edm: . @prefix dcterms: . @prefix dc: . @prefix skos: . @prefix ns0: . vivo:departmentOrSchool "Non UBC"@en ; edm:dataProvider "DSpace"@en ; dcterms:creator "Viray, Bianca"@en ; dcterms:issued "2017-11-26T22:01:21"@en, "2017-05-30T15:01"@en ; dcterms:description """Let $Y$ be a principal homogeneous space of an abelian surface, or a K3 surface, over a finitely generated extension of $\\mathbb{Q}$. In 2008, Skorobogatov and Zarhin showed that the Brauer group modulo algebraic classes $\\mathrm{Br}{Y}/ \\mathrm{Br}_1{Y}$ is finite. We study this quotient for the family of surfaces that are geometrically isomorphic to a product of isogenous non-CM elliptic curves, as well as the related family of geometrically Kummer surfaces; both families can be characterized by their geometric N\\'eron-Severi lattices. Over a field of characteristic 0, we prove that the existence of a strong uniform bound on the size of the odd-torsion of $\\mathrm{Br}{Y}/ \\mathrm{Br}_1{Y}$ is equivalent to the existence of a strong uniform bound on integers $n$ for which there exist non-CM elliptic curves with abelian $n$-division fields. Using the same methods we show that, for a fixed prime $p$, a number field $k$ of fixed degree $r$, and a fixed discriminant of the geometric N\\'eron-Severi lattice, $(\\mathrm{Br}{Y} / \\mathrm{Br}_1{Y})[p^\\infty]$ is bounded by a constant that depends only on $p$, $r$, and the discriminant. This is joint work with Anthony Várilly-Alvarado."""@en ; edm:aggregatedCHO "https://circle.library.ubc.ca/rest/handle/2429/63731?expand=metadata"@en ; dcterms:extent "50 minutes"@en ; dc:format "video/mp4"@en ; skos:note ""@en, "Author affiliation: University of Washington"@en ; edm:isShownAt "10.14288/1.0360734"@en ; dcterms:language "eng"@en ; ns0:peerReviewStatus "Unreviewed"@en ; edm:provider "Vancouver : University of British Columbia Library"@en ; dcterms:publisher "Banff International Research Station for Mathematical Innovation and Discovery"@en ; dcterms:rights "Attribution-NonCommercial-NoDerivatives 4.0 International"@en ; ns0:rightsURI "http://creativecommons.org/licenses/by-nc-nd/4.0/"@en ; ns0:scholarLevel "Faculty"@en ; dcterms:isPartOf "BIRS Workshop Lecture Videos (Banff, Alta)"@en ; dcterms:subject "Mathematics"@en, "Number theory"@en, "Algebraic geometry"@en, "Arithmetic number theory"@en ; dcterms:title "Abelian n-division fields of elliptic curves and Brauer groups of product Kummer and abelian surfaces"@en ; dcterms:type "Moving Image"@en ; ns0:identifierURI "http://hdl.handle.net/2429/63731"@en .