Brauer groups of Kummer surfaces arising from elliptic curves with complex multiplication

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dc.contributor.advisorVárilly-Alvarado, Anthonyen_US
dc.creatorJohnson, Alexis Katherineen_US
dc.date.accessioned2019-05-16T19:28:41Zen_US
dc.date.available2019-05-16T19:28:41Zen_US
dc.date.created2019-05en_US
dc.date.issued2019-04-19en_US
dc.date.submittedMay 2019en_US
dc.date.updated2019-05-16T19:28:41Zen_US
dc.description.abstractThe Brauer group of a variety often captures arithmetic information about the space. In this thesis, we study the Brauer group of a special kind of K3 surface, namely, a Kummer surface associated with a self-product of an elliptic curve over a number field with complex multiplication by a non-maximal order in an imaginary quadratic number field. Skorobogatov has conjectured that the Brauer group controls the existence of rational points on K3 surfaces. In practice, given a K3 surface, one often needs explicit descriptions of Brauer elements in order to study the behavior of rational points. The surfaces studied in this thesis have a geometrically rich structure that enables us to explicitly compute both the algebraic and transcendental Brauer groups over the rational numbers. Furthermore, over arbitrary number fields, we bound the transcendental Brauer group.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.citationJohnson, Alexis Katherine. "Brauer groups of Kummer surfaces arising from elliptic curves with complex multiplication." (2019) Diss., Rice University. <a href="https://hdl.handle.net/1911/105424">https://hdl.handle.net/1911/105424</a>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/105424en_US
dc.language.isoengen_US
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.en_US
dc.subjectBrauer groupsen_US
dc.subjectK3 surfacesen_US
dc.subjectelliptic curvesen_US
dc.subjectalgebraic number theoryen_US
dc.subjectalgebraic geometryen_US
dc.titleBrauer groups of Kummer surfaces arising from elliptic curves with complex multiplicationen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentMathematicsen_US
thesis.degree.disciplineNatural Sciencesen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelDoctoralen_US
thesis.degree.nameDoctor of Philosophyen_US
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