From: rgep@pmms.cam.ac.uk (Richard Pinch)
Newsgroups: sci.math
Subject: Re: Taniyama Conjecture generality
Date: 1 Feb 1995 11:00:00 GMT
Keywords: Shimura-Taniyama-Weil conjecture; semi-stable reduction

In article <1995Jan31.155219.16286@il.us.swissbank.com>, 
mgriffin@il.us.swissbank.com (Mike Griffin) writes:
|> Today's New York Times has a piece by Gina Kolata 
 > in which it is reported that Wiles'  
|> proof of the Taniyama conjecture has already been 
 > extend to a larger class of curves than  
|> the semi-stable ones.
|> 
|> Can anyone state what the larger class is (in terms 
 > comprehensible to, say, a first-year  
|> graduate student)?

Fred Diamond (here in Cambridge) has extended it to all
curves whose reduction at 3 and 5 is semi-stable.  That
is, the curve mod 3 or mod 5 either remains an elliptic
curve (no singularities) or the singularity is a double
point (such as Y^2 = X^3 - X^2) rather than a cusp (such
as Y^2 = X^3).

Richard Pinch;  Queens' College, Cambridge