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By J. S. Milne

This quantity offers for the 1st time entire proofs of the elemental mathematics duality theorems that experience come to play an more and more very important function in quantity idea and mathematics geometry. bankruptcy 1 is dedicated to an exposition of those theorems within the Galois cohomology of quantity fields introduced through Tate in 1962 and describes later paintings within the similar zone. The dialogue assumes just a wisdom of easy Galois cohomology and sophistication box theory.Chapter 2 specializes in the paintings of Artin and Verdier who re-interpreted and built Tate's principles within the framework of etale cohomology; the various more moderen advancements during this sector also are covered.Finally, in bankruptcy three, which incorporates a couple of new effects, it truly is proven how flat cohomology is required so as to turn out and to use duality theorems in relation to teams that have torsion of order divisible by way of one of many residue features.

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