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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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    http://hdl.handle.net/10217/68201
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    Abstract
    The 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 ...
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    Author(s)
    Williams, Cassandra L.

    Advisor(s)
    Achter, Jeffrey

    Date Issued
    2012
    Format
    born digital; doctoral dissertations
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    • 2000-2019 - CSU Theses and Dissertations
    • Theses and Dissertations - Department of Mathematics

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