New maximal curves as ray class fields over Deligne-Lusztig curves

Quotient Curves of the Deligne-lusztig Curve of Suzuki Type

Inspired by a recent paper of Garcia, Stichtenoth and Xing [2000, Compositio Math. 120, 137–170], we investigate the quotient curves of the Deligne-Lusztig curve associated to the Suzuki group Sz(q).

Deligne-lusztig Varieties and Period Domains over Finite Fields

Let G0 be a reductive group over Fq. There are two classes of algebraic varieties over an algebraic closure F of Fq attached to G0. Let us recall their definition. We set G = G0×Fq F. To G there is associated the maximal torus, the Weyl group W and the set of fundamental reflections in W , cf. [DL] 1.1. Let X = XG be the set of all Borel subgroups of G. Then X is a smooth projective algebraic v...

On maximal curves over finite fields of small order

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