Tours ramifiées infinies de corps de classes

AbstractThe 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