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Explicit descent setups

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If you have a question about this talk, please contact Tom Fisher.

The first step in computing the group of rational points on a Jacobian of an algebraic curve over a global field is to compute the free rank of that group. The most common method does that by computing a Selmer group. While in principle effectively computable, one needs to specify extra data to do so in practice. We will present a description of such data, called an explicit descent setup, that covers all cases in the literature to date.

It is surprising how little information explicit descent setups yield about Selmer groups in general. There are various additional obstructions one needs to deal with as well. In cases considered previously, many of these turn out to be trivial, but when one adapts these methods for Jacobians of smooth plane quartics then it is easy to find examples where these obstructions play a role.

This talk is part of the Number Theory Seminar series.

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