TY - JOUR
T1 - Enumeration of certain varieties over a finite field
AU - Friedlander, John B.
AU - Shparlinski, Igor E.
PY - 2014/8/1
Y1 - 2014/8/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84924777574&partnerID=8YFLogxK
U2 - 10.1090/S0002-9939-2014-11999-X
DO - 10.1090/S0002-9939-2014-11999-X
M3 - Article
AN - SCOPUS:84924777574
VL - 142
SP - 2615
EP - 2623
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
SN - 0002-9939
IS - 8
ER -