Differences between revisions 1 and 2
 ⇤ ← Revision 1 as of 2007-09-30 13:36:34 → Size: 259 Editor: KiranKedlaya Comment: ← Revision 2 as of 2007-10-03 18:01:25 → ⇥ Size: 792 Editor: KiranKedlaya Comment: Deletions are marked like this. Additions are marked like this. Line 1: Line 1: Put together a p-adic heights calculator for hyperelliptic curves. 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. Line 3: Line 6: Develop a version of Harvey's algorithm for computing Coleman integrals. 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.) Line 5: Line 9: Come up with a good framework for doing iterated Coleman integrals (for use in the nonabelian Chabauty method). 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).

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)