scholarly journals Classification of characteristic polynomials of simple supersingular abelian varieties over finite fields

2014 ◽  
Vol 51 (2) ◽  
pp. 415-436 ◽  
Author(s):  
Vijaykumar Singh ◽  
Gary McGuire ◽  
Alexey Zaytsev
Keyword(s):  
Finite Fields ◽  
Abelian Varieties ◽  
Characteristic Polynomials

scholarly journals CHARACTERISTIC POLYNOMIALS OF SIMPLE ORDINARY ABELIAN VARIETIES OVER FINITE FIELDS

2021 ◽  
pp. 1-7
Author(s):  
LENNY JONES
Keyword(s):  
Finite Field ◽  
Finite Fields ◽  
Abelian Varieties ◽  
Characteristic Polynomials ◽  
Easy Method

Abstract We provide an easy method for the construction of characteristic polynomials of simple ordinary abelian varieties ${{\mathcal A}}$ of dimension g over a finite field ${{\mathbb F}}_q$ , when $q\ge 4$ and $2g=\rho ^{b-1}(\rho -1)$ , for some prime $\rho \ge 5$ with $b\ge 1$ . Moreover, we show that ${{\mathcal A}}$ is absolutely simple if $b=1$ and g is prime, but ${{\mathcal A}}$ is not absolutely simple for any prime $\rho \ge 5$ with $b>1$ .

scholarly journals Classification of nonrigid families of abelian varieties

1993 ◽  
Vol 45 (2) ◽  
pp. 159-189
Author(s):  
Masa-Hiko Saitō
Keyword(s):  
Abelian Varieties

scholarly journals Counting Points on Curves and Abelian Varieties Over Finite Fields

2001 ◽  
Vol 32 (3) ◽  
pp. 171-189 ◽  
Author(s):  
Leonard M. Adleman ◽  
Ming-Deh Huang
Keyword(s):  
Finite Fields ◽  
Abelian Varieties ◽  
Counting Points
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