From buzzard@ihp.jussieu.fr Fri Apr 28 04:35 PDT 2000 Received: from shiva.jussieu.fr (shiva.jussieu.fr [134.157.0.129]) by math.berkeley.edu (8.9.3/8.9.3) with ESMTP id EAA27862 for ; Fri, 28 Apr 2000 04:35:00 -0700 (PDT) Received: from pclinux1.ihp.jussieu.fr (IDENT:postfix@pclinux1.ihp.jussieu.fr [134.157.86.76]) by shiva.jussieu.fr (8.10.0/jtpda-5.3.3) with ESMTP id e3SBYjU38672 for ; Fri, 28 Apr 2000 13:34:45 +0200 (CEST) Received: by pclinux1.ihp.jussieu.fr (Postfix, from userid 644) id 6AEEB88058; Fri, 28 Apr 2000 13:34:45 +0200 (CEST) Received: from localhost (localhost [127.0.0.1]) by pclinux1.ihp.jussieu.fr (Postfix) with ESMTP id 60D5F88057 for ; Fri, 28 Apr 2000 13:34:45 +0200 (CEST) Date: Fri, 28 Apr 2000 13:34:45 +0200 (CEST) From: Kevin Buzzard To: "William A. Stein" Subject: Re: Modular Symbols handbook In-Reply-To: <390A6416.F440605@mail.math.berkeley.edu> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Content-Length: 785 Oh, PS: > eps:=DirichletCharacter(9,[3]); > M:=ModularSymbols(eps,10,-1); Creating M_10(Gamma_1(9),eps;F_0)^- , 1.269 seconds. > T:=Tn(Sk(M),3); Tn( M: Full Vector space of degree 8 over Cyclotomic Field of order..., n: 3 ) HeckeOperator( M: Full Vector space of degree 8 over Cyclotomic Field of order..., n: 3 ) HeckeOperator( M: Full Vector space of degree 8 over Cyclotomic Field of order..., Heil: [ [ 1, 0, 0, 3 ], [ 3, 1, 0, 1 ], [ 1, 0, 1, 3 ], [ 3, 0, 0,... ) In file "/home/buzzard/maths/computers/magma/magma/Hecke/hecke.m", line 1036, column 14: >> F := M`F; ^ Runtime error in `: Attribute 'F' for this structure is valid but not assigned > From buzzard@ihp.jussieu.fr Fri Apr 28 04:38 PDT 2000 Received: from shiva.jussieu.fr (shiva.jussieu.fr [134.157.0.129]) by math.berkeley.edu (8.9.3/8.9.3) with ESMTP id EAA27846 for ; Fri, 28 Apr 2000 04:34:18 -0700 (PDT) Received: from pclinux1.ihp.jussieu.fr (IDENT:postfix@pclinux1.ihp.jussieu.fr [134.157.86.76]) by shiva.jussieu.fr (8.10.0/jtpda-5.3.3) with ESMTP id e3SBXwU38480 for ; Fri, 28 Apr 2000 13:33:58 +0200 (CEST) Received: by pclinux1.ihp.jussieu.fr (Postfix, from userid 644) id CF97788058; Fri, 28 Apr 2000 13:33:58 +0200 (CEST) Received: from localhost (localhost [127.0.0.1]) by pclinux1.ihp.jussieu.fr (Postfix) with ESMTP id B7F2288057 for ; Fri, 28 Apr 2000 13:33:58 +0200 (CEST) Date: Fri, 28 Apr 2000 13:33:58 +0200 (CEST) From: Kevin Buzzard To: "William A. Stein" Subject: Re: Modular Symbols handbook In-Reply-To: <390A6416.F440605@mail.math.berkeley.edu> Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Content-Length: 491 I'll try and take a look at it. I don't have 1/10th the time I used to have though. Ironically, having 1/10th the time I used to have has made me more focussed, ignoring emails that can safely be ignored and putting more time into work when I have time. So I sat down and read through all of the artin thing. I want to finish it before I do anything else. I will try and type up the final version within the next few days. I have some questions but they're at home and I'm at work. Kevin From buzzard@ihp.jussieu.fr Fri Apr 28 04:39 PDT 2000 Received: from shiva.jussieu.fr (shiva.jussieu.fr [134.157.0.129]) by math.berkeley.edu (8.9.3/8.9.3) with ESMTP id EAA27933 for ; Fri, 28 Apr 2000 04:39:16 -0700 (PDT) Received: from pclinux1.ihp.jussieu.fr (IDENT:postfix@pclinux1.ihp.jussieu.fr [134.157.86.76]) by shiva.jussieu.fr (8.10.0/jtpda-5.3.3) with ESMTP id e3SBclU39553 for ; Fri, 28 Apr 2000 13:38:48 +0200 (CEST) Received: by pclinux1.ihp.jussieu.fr (Postfix, from userid 644) id 35F0A88057; Fri, 28 Apr 2000 13:38:48 +0200 (CEST) Received: from localhost (localhost [127.0.0.1]) by pclinux1.ihp.jussieu.fr (Postfix) with ESMTP id 28BFF88053 for ; Fri, 28 Apr 2000 13:38:48 +0200 (CEST) Date: Fri, 28 Apr 2000 13:38:48 +0200 (CEST) From: Kevin Buzzard To: "William A. Stein" Subject: Re: Modular Symbols handbook In-Reply-To: Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Content-Length: 680 PPS I gave a talk here at IHP about patterns in slopes and now people are pestering me to do lots of things that I can't do immediately because I can't work out newton polys of polys defined over the integers of cyclotomic fields. If there's a way of (a) persuading them into Q_p(zeta) from Q(zeta) (b) accessing a valuation function in Q_p(zeta) then presumably NewtonSlopes would be easy to adapt so that it works in this case. Can this be done? I guess I should find out myself... Kevin PS I remember one of the questions I had about Buzzard-Stein: if you believe this "Buzzard Bound" then how many of those A_5 extns can we unconditionally prove come from modular forms? From k.buzzard@ic.ac.uk Fri Apr 28 05:33 PDT 2000 Received: from judy.ic.ac.uk (judy.ic.ac.uk [155.198.5.28]) by math.berkeley.edu (8.9.3/8.9.3) with ESMTP id FAA29102 for ; Fri, 28 Apr 2000 05:33:21 -0700 (PDT) Received: from juliet.ic.ac.uk ([155.198.5.4]) by judy.ic.ac.uk with esmtp (Exim 2.12 #1) id 12l9xK-0001wF-00 for was@math.berkeley.edu; Fri, 28 Apr 2000 13:33:14 +0100 Received: from geometry.ma.ic.ac.uk ([155.198.192.7]) by juliet.ic.ac.uk with esmtp (Exim 2.12 #1) id 12l9xL-0004aM-00 for was@math.berkeley.edu; Fri, 28 Apr 2000 13:33:15 +0100 Received: from thatcher.ma.ic.ac.uk ([155.198.194.52] ident=kbuzzard) by geometry.ma.ic.ac.uk with smtp (Exim 2.12 #1) id 12l9wB-0000yy-00 for was@math.berkeley.edu; Fri, 28 Apr 2000 13:32:03 +0100 Date: Fri, 28 Apr 2000 13:33:11 +0100 (bst) From: Kevin Buzzard X-Sender: kbuzzard@thatcher.ma.ic.ac.uk To: was@math.berkeley.edu Subject: ! Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Content-Length: 262 Actually I just discovered that the Valuation command is pretty flexible. All I have to do is to rewrite NewtonSlopes a little, so it doesn't want p as an input. It's quite easy. > K:=CyclotomicField(3); > IsPrime(zeta-1); false Is that right??? Kevin From k.buzzard@ic.ac.uk Fri Apr 28 06:05 PDT 2000 Received: from judy.ic.ac.uk (judy.ic.ac.uk [155.198.5.28]) by math.berkeley.edu (8.9.3/8.9.3) with ESMTP id GAA29705 for ; Fri, 28 Apr 2000 06:05:48 -0700 (PDT) Received: from juliet.ic.ac.uk ([155.198.5.4]) by judy.ic.ac.uk with esmtp (Exim 2.12 #1) id 12lASm-0002gZ-00 for was@math.berkeley.edu; Fri, 28 Apr 2000 14:05:44 +0100 Received: from geometry.ma.ic.ac.uk ([155.198.192.7]) by juliet.ic.ac.uk with esmtp (Exim 2.12 #1) id 12lASk-0005Ig-00 for was@math.berkeley.edu; Fri, 28 Apr 2000 14:05:42 +0100 Received: from thatcher.ma.ic.ac.uk ([155.198.194.52] ident=kbuzzard) by geometry.ma.ic.ac.uk with smtp (Exim 2.12 #1) id 12lARa-00013b-00 for was@math.berkeley.edu; Fri, 28 Apr 2000 14:04:30 +0100 Date: Fri, 28 Apr 2000 14:05:39 +0100 (bst) From: Kevin Buzzard X-Sender: kbuzzard@thatcher.ma.ic.ac.uk To: was@math.berkeley.edu Subject: :-) Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Content-Length: 884 Now I've spent 2 minutes writing a NewtonSlopes myself, we see already something that nobody seems to have realised: the eigencurve for p=3 is also etale round the edges. Not only that, it appears to be a disjoint union of copies of weight space. How else could one explain: > eps:=DirichletCharacter(27,[9]); > K:=CyclotomicField(9); > M:=ModularSymbols(eps,6,-1); Creating M_6(Gamma_1(27),eps;F_0)^- , 12.839 seconds. > T:=Tn(M,3); > f:=CharacteristicPolynomial(T); > NewtonSlopes(f,z-1); [* 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28 *] (note that I've increased the scope of NewtonSlopes: the fact that I was too lazy to do this before meant that I'd never spotted this). So I reckon that for general p this will also hold! It's hard to say when this idea would have come to light without Hecke as a resource :-) Now I have my new toy I can check some more. Kevin From maggie925@hotmail.com Fri Apr 28 07:28 PDT 2000 Received: from hotmail.com (f65.law7.hotmail.com [216.33.237.65]) by math.berkeley.edu (8.9.3/8.9.3) with SMTP id HAA02315 for ; Fri, 28 Apr 2000 07:28:46 -0700 (PDT) Received: (qmail 179 invoked by uid 0); 28 Apr 2000 14:28:16 -0000 Message-ID: <20000428142816.178.qmail@hotmail.com> Received: from 129.78.64.5 by www.hotmail.com with HTTP; Fri, 28 Apr 2000 07:28:15 PDT X-Originating-IP: [129.78.64.5] From: "Maggie Wong" To: was@gold.math.berkeley.edu Subject: See ya.... Date: Fri, 28 Apr 2000 14:28:15 GMT Mime-Version: 1.0 Content-Type: text/plain; format=flowed Content-Length: 185 Hi William See you tomorrow!! Mag. ________________________________________________________________________ Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com