Counting points on varieties over finite fields of small characteristic

2006/12/06 by Alan G. B. Lauder, Daqing Wan, Lauder, Alan G. B. +1 · 3 citations
Computer Science · Mathematics · #Cryptography and Residue Arithmetic #Coding theory and cryptography #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.math/0612147

Abstract

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.

Cited by

• Randomized Polynomial-Time Root Counting in Prime Power Rings
• Counting points on surfaces in polynomial time
• Complexity of counting points on curves and the factor P₁(T) of the zeta function of surfaces

Related

• Computing zeta functions over finite fields
• Counting points on curves using a map to P¹, II
• Counting points on curves using a map to P¹
• Complexity of counting points on curves and the factor P₁(T) of the zeta function of surfaces
• Using zeta functions to factor polynomials over finite fields