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This is a note of talks I gave at the number theory seminar at TsinghuaUniversity in Fall 2011.  We will introduce the local and global Euler characteristic formulas given byJohn Tate(1962) for Galois cohomology. We will give a detailed proof based onthe idea in Hida's book[1,ch4.4.5] and Milne's book[2,ch1.5].

Introduction to Local and Global Euler Characteristic Formulas