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Galois cohomology in degree 3 of function fields of curves over number fields

✍ Scribed by V. Suresh

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
290 KB
Volume
107
Category
Article
ISSN
0022-314X

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✦ Synopsis

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 Þ; where for any lAk Γƒ ; Γ°lÞ denotes the image of k Γƒ in H 1 Γ°k; Z=2Þ: In this paper we prove a higher dimensional analogue of the Tate's lemma.

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