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On the curves y2 = f(x), without Riemann-Roch
by
Jack Ohm
Louisiana State University
The usual approach to curves of the form y2 = f(x) is to separate them into rational, elliptic, and hyperelliptic curves by means of genus and then apply Riemann-Roch to discover some of their properties. While Riemann-Roch and the notion of genus are powerful tools, they represent a long and involved story. I shall show here that one can at least make some initial observations about these curves using only techinques from valuation theory.
Date received: April 30, 1999
Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacv-40.