Counting points on varieties over finite fields of small characteristic

Details Counting points on varieties over finite fields of small characteristic Counting points on varieties over finite fields of small characteristic

2006-12-06

arxiv.org/abs/math/0612147v1

Mathematics

Number Theory

To appear in: "Algorithmic number theory: lattices, number fields, curves and cryptography", J.P. Buhler and P. Stevenhagen (e

Scientific paper

We present a deterministic polynomial time algorithm for computing the zeta function of an arbitrary variety of fixed dimension over a finite field of small characteristic. One consequence of this result is an efficient method for computing the order of the group of rational points on the Jacobian of a smooth geometrically connected projective curve over a finite field of small characteristic.

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