Space filling curves over finite fields

Space Filling Curves over Finite Fields

In this note, we construct curves over finite fields which have, in a certain sense, a “lot” of points, and give some applications to the zeta functions of curves and abelian varieties over finite fields. In fact, we found the basic construction, given in Lemma 1, of curves in A which go through every rational point, as part of an unsuccessful attempt to find curves of growing genus over a fixe...

Elliptic Curves over Finite Fields

In this chapter, we study elliptic curves defined over finite fields. Our discussion will include the Weil conjectures for elliptic curves, criteria for supersingularity and a description of the possible groups arising as E(Fq). We shall use basic algebraic geometry of elliptic curves. Specifically, we shall need the notion and properties of isogenies of elliptic curves and of the Weil pairing....

Elliptic Curves over Finite Fields

Counting curves over finite fields

Article history: Received 25 August 2014 Received in revised form 10 September 2014 Accepted 18 September 2014 Available online 4 November 2014 Communicated by H. Stichtenoth MSC: 11G20 10D20 14G15 14H10

Coverings of singular curves over finite fields