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A Finiteness Theorem in the Galois Cohomology of Algebraic Number Fields

✍ Scribed by Wayne Raskind


Book ID
125691091
Publisher
American Mathematical Society
Year
1987
Tongue
English
Weight
185 KB
Volume
303
Category
Article
ISSN
0002-9947

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Let k be a field of characteristic not equal to 2. For nZ1; let H n Γ°k; Z=2Þ denote the nth Galois Cohomology group. The classical Tate's lemma asserts that if k is a number field then given finitely many elements a 1 ; ?; a n AH 2 Γ°k; Z=2Þ; there exist a; b 1 ; ?; b n Ak Γƒ such that a i ΒΌ Γ°aÞ,Γ°b i