Professor Mazur has asked me to warn everyone that the conventions in the third set of notes change somewhere in the middle; this isn't really a serious issue.

Preliminary lecture schedule (dates are not yet entirely clear):

Mak Trifkovic and Brian Osserman - Review of some algebraic number theory, introduction to Galois modules including elliptic curve examples, introduction to cohomology of groups and cup product, introduction to Galois cohomology, and specifically for finite fields and beginning discussion of local fields.

Pete Clark - Local fields, a discussion of the structure of the Galois groups of the algebraic closure of local fields, and higher ramification groups.

David Jao and Alex Popa - Back to group cohomology, Galois modules, interpretation of the first cohomology group, introduction to Tate local duality.

Marty Weissman - Tate local duality.

Stephanie Yang - Galois cohomology of global fields, local "conditions", introduction to the Selmer group, examples.

Alex Ghitza and Nick Rogers - The Selmer group, finite generation of the Selmer group, introduction to elliptic curve and abelian variety examples.

Paul Ellis and Yu-Ru Liu - Abelian varieties and their cohomology, examples. Introduction to their Galois representations on torsion points.

Tom Weston - An overview of a theorem of Flach

These are my notes for the 1997 course. As of September 20, 1999 I have posted new versions of the first 16 lectures. The changes are mostly minor. The largest changes are to Lecture 4, which I hope is now slightly more comprehensible, and Lectures 13-16, where I have removed the assumption that the coefficient rings are integral domains. I would appreciate notification of any errors at: [email protected]

These are some additional write-ups of mine which are referred to in the notes above.