We consider the problem of counting the number of points on a plane curve, defined by a homogeneous polynomial F (x, y, z) โ Fq[x, y, z], which are rational over a ground field Fq. More precisely, we show that if we are given a projective plane curve C of degree n, and if C has only ordinary multipl
On the K-theory of curves over finite fields
โ Scribed by Kevin R. Coombes
- Publisher
- Elsevier Science
- Year
- 1988
- Tongue
- English
- Weight
- 488 KB
- Volume
- 51
- Category
- Article
- ISSN
- 0022-4049
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
We show that SK 1 X = 0 for every affine curve X over a finite field.
In this paper we introduce a definition for L-functions associated to an Abelian covering of algebraic curves with singularities. The main result is a proof that this definition is compatible with the definition of the zeta function of a singular curve.
Let A be a finite abelian group such that there is an elliptic curve defined over a finite field F q with E(F q )$A. We will determine the possible group structures E(F q k) as E varies over all elliptic curves defined over F q with E(F q )$A.
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 over Fq, we improve Pila's result and show that the pro