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Conjugacy classes of matrix groups over local rings and an application to the enumeration of abelian varieties

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dc.contributor.authorWilliams, Cassandra L., author
dc.contributor.authorAchter, Jeffrey, advisor
dc.contributor.authorEykholt, Richard, committee member
dc.contributor.authorHulpke, Alexander, committee member
dc.contributor.authorPenttila, Tim, committee member
dc.date.accessioned2007-01-03T08:11:29Z
dc.date.available2007-01-03T08:11:29Z
dc.date.issued2012
dc.description.abstractThe Frobenius endomorphism of an abelian variety over a finite field Fq of dimension g can be considered as an element of the finite matrix group GSp2g(Z/lr). The characteristic polynomial of such a matrix defines a union of conjugacy classes in the group, as well as a totally imaginary number field K of degree 2g over Q. Suppose g = 1 or 2. We compute the proportion of matrices with a fixed characteristic polynomial by first computing the sizes of conjugacy classes in GL2(Z/lr) and GSp4(Z/lr. Then we use an equidistribution assumption to show that this proportion is related to the number of abelian varieties over a finite field with complex multiplication by the maximal order of K via a theorem of Everett Howe.
dc.format.mediumborn digital
dc.format.mediumdoctoral dissertations
dc.identifierWilliams_colostate_0053A_11267.pdf
dc.identifierETDF2012400361MATH
dc.identifier.urihttp://hdl.handle.net/10217/68201
dc.languageEnglish
dc.language.isoeng
dc.publisherColorado State University. Libraries
dc.relation.ispartof2000-2019
dc.rightsCopyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright.
dc.subjectabelian variety
dc.subjectGSp4
dc.subjectconjugacy class
dc.subjectcomplex multiplication
dc.titleConjugacy classes of matrix groups over local rings and an application to the enumeration of abelian varieties
dc.typeText
dcterms.rights.dplaThis Item is protected by copyright and/or related rights (https://rightsstatements.org/vocab/InC/1.0/). You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
thesis.degree.disciplineMathematics
thesis.degree.grantorColorado State University
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy (Ph.D.)

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