Enumeration of certain varieties over a finite field

John B. Friedlander*, Igor E. Shparlinski

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Let Fqbe a finite field of q elements. E. Howe has shown that there is a natural correspondence between the isogeny classes of two-dimensional ordinary abelian varieties over Fq which do not contain a principally polarized variety and pairs of positive integers (a, b) satisfying q = a2+ b, where gcd(q, b) = 1 and all prime divisors l of b are in the arithmetic progression l ≡ 1 (mod 3). This arithmetic criterion allows us to give good upper bounds, and for many finite fields good lower bounds, for the frequency of occurrence of isogeny classes of varieties having this property.

Original languageEnglish
Pages (from-to)2615-2623
Number of pages9
JournalProceedings of the American Mathematical Society
Issue number8
Publication statusPublished - 1 Aug 2014


Dive into the research topics of 'Enumeration of certain varieties over a finite field'. Together they form a unique fingerprint.

Cite this