Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Path: utzoo!linus!decvax!decwrl!goldberg From: goldberg@decwrl.UUCP (David Goldberg) Newsgroups: net.math Subject: The Mordell Conjecture Message-ID: <2687@decwrl.UUCP> Date: Tue, 19-Jul-83 18:17:13 EDT Article-I.D.: decwrl.2687 Posted: Tue Jul 19 18:17:13 1983 Date-Received: Wed, 20-Jul-83 01:15:39 EDT Lines: 15 The Mordell conjecture says that if you have a polynonmial in two variables with rational coefficients (like x^n - y^n - 1) and if when you think of it as a Riemann surface it has genus >= 2, then it has finitely many rational solutions. If you take the Fermat equation x^n + y^n = z^n, and divide by z^n, you get the equation t^n + s^n - 1 = 0, where t = (x/z) and s = (y/z). When n > 2, its genus is >=2, so the Mordell conjecture implies that for each n > 2, Fermat's equation has at most finitely many solutions. Faltings has circulated a preprint of his proof of the Mordell conjecture, but it hasn't been independently checked yet. david goldberg {decvax, ucbvax}!decwrl!goldberg