Frobenius maps of Abelian varieties and finding roots of unity in finite fields

@article{Pila1990FrobeniusMO,
  title={Frobenius maps of Abelian varieties and finding roots of unity in finite fields},
  author={J. Pila},
  journal={Mathematics of Computation},
  year={1990},
  volume={55},
  pages={745-763}
}
  • J. Pila
  • Published 1990
  • Mathematics
  • Mathematics of Computation
"If 'twere done when 'tis done, then 'twere well/ It were done quickly."-Macbeth. Abstract. We give a generalization to Abelian varieties over finite fields of the algorithm of Schoof for elliptic curves. Schoof showed that for an elliptic curve E over F , given by a Weierstrass equation, one can compute the number of Q F -rational points of E in time 0((log<?) ). Our result is the following. Let A be an Abelian variety over F. Then one can compute the characteristic polynomial of the Frobenius… Expand
188 Citations
Counting Points on an Abelian Variety over a Finite Field
Horizontal isogeny graphs of ordinary abelian varieties and the discrete logarithm problem
Explicit CM-theory in dimension 2
Reduced Ideals in Function Fields
Counting points on hyperelliptic curves with explicit real multiplication in arbitrary genus
  • S. Abelard
  • Mathematics, Computer Science
  • J. Complex.
  • 2020
Counting Points on Curves and Abelian Varieties Over Finite Fields
Counting Points on Curves over Finite Fields
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 33 REFERENCES
Elliptic Curves Over Finite Fields and the Computation of Square Roots mod p
Factoring Polynomials Over Algebraic Number Fields
Factorization of polynomials over finite fields and factorization of primes in algebraic number fields
Recognizing primes in random polynomial time
Factoring Polynomials Over Algebraic Number Fields
  • S. Landau
  • Mathematics, Computer Science
  • SIAM J. Comput.
  • 1985
Riemann hypothesis and finding roots over finite fields
Almost all primes can be quickly certified
Foundations of Algebraic Geometry
...
1
2
3
4
...