From: "Dino J. Lorenzini" <dino@math.unc.edu>
Received: (from dino@localhost)
	by noether.math.unc.edu (8.9.3/8.9.3) id QAA05306;
	Fri, 28 May 1999 16:30:41 -0400 (EDT)
Date: Fri, 28 May 1999 16:30:41 -0400 (EDT)
Message-Id: <199905282030.QAA05306@noether.math.unc.edu>
To: was@math.berkeley.edu
Subject: Re: Component groups
Cc: dino@math.unc.edu
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Dear William,

Sorry for the delay in answering.
Your formula is very interesting, and I had not seen it before.
Regarding my manuscript, it is still unpublished. Yours
looking at it is encouraging me to do something about it!

Regarding your question on surjectivity of maps 
of component groups, I do not know much about it, 
but it is certainly worth looking at it.  
In the case of strong Weil curves, it looks from the tables that the group
of components has order 1 or 2 if p >37; is that a true fact?
coming for instance from your formula when N=p? Do you also get small orders
for the group of components of A_f when p is large?

Note that when N=p^2, the map is not surjective
even in the case of elliptic curves: take p=11.
Then the order for \Phi is p^2-1/24 = 5, while it has elliptic quotients
with groups of order 2.

Do I gather that you plan to graduate next year? Do not
forget to send me a copy of your thesis when it is ready.

Please send my regards to Ken,

Have a good summer,

Dino