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SUMMARY:Explicit descent setups - Nils Bruin (Simon Fraser)
DTSTART:20110308T143000Z
DTEND:20110308T153000Z
UID:TALK28539@talks.cam.ac.uk
CONTACT:Tom Fisher
DESCRIPTION:The first step in computing the group of rational points on a\
 nJacobian of an algebraic curve over a global field is to compute the free
 \nrank of that group. The most common method does that by computing a Selm
 er\ngroup. While in principle effectively computable\, one needs to specif
 y extra\ndata to do so in practice. We will present a description of such 
 data\,\ncalled an explicit descent setup\, that covers all cases in the li
 terature to\ndate.\n\nIt is surprising how little information explicit des
 cent setups yield about\nSelmer groups in general. There are various addit
 ional obstructions one\nneeds to deal with as well. In cases considered pr
 eviously\, many of these\nturn out to be trivial\, but when one adapts the
 se methods for Jacobians of\nsmooth plane quartics then it is easy to find
  examples where these\nobstructions play a role.\n
LOCATION:MR13
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