Hello! Do you have success with reduction at p=2? Do you know some way to calculate it using Sage?
P.S. I've asked a question at mathoverflow: http://mathoverflow.net/questions/171708/calculate-reduction-of-jacobian-of-hyperelliptic-curve суббота, 4 июля 2009 г., 2:12:52 UTC+4 пользователь Tim Dokchitser написал: > > > >> +1 to David's remark. ALSO, see Tim Dokchiter's paper(s) on > > >> computing > > >> L-series. Maybe part of the point of them is to "reverse engineer" > > >> information about bad factors from knowledge of good factors, when > > >> possible. I'll let Tim comment further. > > > > Tim, anything you'd care to add would be appreciated. > > As William says, it is occasionally possible to reverse-engineer bad > factors from the functional equation of the L-function. Say you have a > curve C for which you know all bad factors except at p=2, where C has > some horrible reduction type. Then you can try to go through possible > exponents of the conductor at 2 (it is bounded by that of the > discriminant) and possible local factors at 2 (again, there are > finitely many choices) and check the functional equation of the L- > series of C - there is only one choice where it is satisfied, and that > is the correct one. > > There is an examples in Magma, > http://magma.maths.usyd.edu.au/magma/htmlhelp/text1412.htm#14432 > that works with an L-series of a genus 2 curve (except that here I > honestly work out the exponent of the conductor and the local factor > at the bad prime, they are harmless here so there is no guessing); > maybe this one may be modified to suit your example. Actually, if you > have a specific hyperelliptic curve in mind, you can send it to me and > I can try to figure out the bad local factors using my old scripts, if > I can remember what they did... > > (As William said, stuff like this is mentioned in > http://arxiv.org/abs/math/0207280, > in section 7) > > Hope this helps! > > Tim > -- You received this message because you are subscribed to the Google Groups "sage-nt" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send an email to [email protected]. Visit this group at http://groups.google.com/group/sage-nt. For more options, visit https://groups.google.com/d/optout.
