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The main goal was to put together a p-adic heights calculator for hyperelliptic curves. Before we have extensions of p-adics, we could:

  • Write a tiny integrals calculator for Weierstrass residue discs.
  • Expand a rational function with poles only in Weierstrass residue discs as a power series.
  • Implement Besser's techniques for calculating with local indices.

After that, we could:

  • Implement full Coleman integration between points defined over extension fields. (Beware: this requires a semilinear version of the fundamental linear system.)

Longer term projects could include:

  • Develop a version of Harvey's algorithm for computing Coleman integrals.
  • Come up with a good framework for doing iterated Coleman integrals (for use in the nonabelian Chabauty method).

days5/proj/coleman (last edited 2008-11-14 13:42:00 by localhost)