论文信息 - Counting Points on Curves and Abelian Varieties Over Finite Fields

Counting Points on Curves and Abelian Varieties Over Finite Fields

We develop efficient methods for deterministic computations with semi-algebraic sets and apply them to the problem of counting points on curves and Abelian varieties over finite fields. For Abelian varieties of dimension g in projective N space overFq, we improve Pila?s result and show that the problem can be solved in O((logq)?) time where ? is polynomial in g as well as in N. For hyperelliptic curves of genus g overFq we show that the number of rational points on the curve and the number of rational points on its Jacobian can be computed in (logq)O(g2logg)time.

Leonard M. Adleman | Ming-Deh A. Huang | L. Adleman

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