A Bayesian approach to computing Brauer groups of cubic surfaces

Simple item page
dc.contributor.advisorVarilly-Alvarado, Anthony
dc.creatorJames, Austen A
dc.date.accessioned2023-01-03T22:33:25Z
dc.date.available2023-01-03T22:33:25Z
dc.date.created2022-12
dc.date.issued2022-12-02
dc.date.submittedDecember 2022
dc.date.updated2023-01-03T22:33:25Z
dc.description.abstractWe present an algorithm for computing the Brauer groups of cubic surfaces. The algorithm takes as input an equation for a cubic surface X and a confidence threshold 0.5 < r < 1 and outputs a candidate for the Brauer group of X and a confidence level > r for the result. The algorithm runs by sampling lifts of Frobenius at many primes of good reduction and relies on Chebotarev’s density theorem and Bayesian inference to produce, with confidence level > r, a subgroup of the Weyl group of E_6. This subgroup represents the action of Galois on the geometric Picard group of X, from which we compute the Brauer group of X. We give a description of this algorithm and a proof that it terminates, as well as an implementation in Magma. We also examine the speed of such an approach relative to existing methods and explore how the Bayesian technique of this algorithm can be applied to answer questions concerning the Galois and Brauer groups of other classes of surfaces.
dc.format.mimetypeapplication/pdf
dc.identifier.citationJames, Austen A. "A Bayesian approach to computing Brauer groups of cubic surfaces." (2022) Diss., Rice University. <a href="https://hdl.handle.net/1911/114191">https://hdl.handle.net/1911/114191</a>.
dc.identifier.urihttps://hdl.handle.net/1911/114191
dc.language.isoeng
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.
dc.subjectarithmetic geometry
dc.subjectbrauer group
dc.subjectcubic surfaces
dc.subjectdel pezzo surfaces
dc.subjectalgebraic geometry
dc.subjectrational points
dc.titleA Bayesian approach to computing Brauer groups of cubic surfaces
dc.typeThesis
dc.type.materialText
thesis.degree.departmentMathematics
thesis.degree.disciplineNatural Sciences
thesis.degree.grantorRice University
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
JAMES-DOCUMENT-2022.pdf
Size:
481.41 KB
Format:
Adobe Portable Document Format
Download
License bundle
Now showing 1 - 2 of 2
No Thumbnail Available
Name:
PROQUEST_LICENSE.txt
Size:
5.84 KB
Format:
Plain Text
Description:
Download
No Thumbnail Available
Name:
LICENSE.txt
Size:
2.61 KB
Format:
Plain Text
Description:
Download
Collections
Rice University Electronic Theses and Dissertations