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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