This
note explains the following topics: Galois Modules, Discrete Valuation
Rings, The Galois Theory of Local Fields, Ramification Groups, Witt Vectors,
Projective Limits of Groups of Units of Finite Fields, The Absolute Galois Group
of a Local Field, Group Cohomology, Galois Cohomology, Abelian Varieties, Selmer
Groups of Abelian Varieties, Kummer Theory, Torsors for Algebraic Groups, The
Main Theorem, Operators on Modular Curves, Heegner Points, Hecke Operators on
Heegner Points and Local Behavior of Cohomology Classes.

**Author(s):** Barry Mazur and Tom Weston

168**Pages**