Marc Perret

Tours ramifiées infinies de corps de classes

Abstract The number A(q) is the upper limit of the maximum number of points of a curve defined over Fq, divided by the genus. A lower bound was established by Serre, using unramified Hilbert class field towers. In this paper, the author gives a conditional criterion of infinitude of ramified class field towers, and applies this result in order to obtain some better lower bounds for A(q). Moreover, the author obtains some slightly weaker unconditional results.

Number of points of Prym varieties over finite fields

We establish some upper and lower bounds for the number of rational points of Prym varieties over finite fields.

Coverings of singular curves over finite fields

We prove that if

On the Number of Points of Some Varieties Over Finite Fields

f : Y\longrightarrow X

Multiplicative character sums and non linear geometric codes

is a finite fiat morphism between two reduced absolutely irreducible algebraic projective curves defined over the finite field

Families of codes exceeding the Varshamov-Gilbert bound

{\sb F}_q

A graph aided strategy to produce good recursive towers over finite fields

, then

A Weil Theorem for singular curves

\mid \sharp Y({\sb F}_q) - \sharp X({\sb F}_q)\mid \leq 2({\pi}_Y - {\pi}_X)\sqrt q,