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Explicit and quantitative results for abelian varieties over finite fields




Krause, Elliot, author
Achter, Jeffrey, advisor
Pries, Rachel, committee member
Juul, Jamie, committee member
Ray, Indrajit, committee member

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Let E be an ordinary elliptic curve over a prime field Fp. Attached to E is the characteristic polynomial of the Frobenius endomorphism, T2 − a1T + p, which controls several of the invariants of E, such as the point count and the size of the isogeny class. As we base change E over extensions Fpn, we may study the distribution of point counts for both of these invariants. Additionally, we look to quantify the rate at which these distributions converge to the expected distribution. More generally, one may consider these same questions for collections of ordinary elliptic curves and abelian varieties.


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elliptic curve
abelian varieties


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