Poitou–Tate duality over extensions of global fields

In this paper, we are interested in the Poitou–Tate duality in Galois cohomology. We will formulate and prove a theorem for a nice class of modules (with a continuous Galois action) over a pro-p ring. The theorem will comprise of the Tate local duality, Poitou–Tate duality and the Poitou–Tateʼs exac...

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Bibliographic Details
Published inJournal of number theory Vol. 132; no. 11; pp. 2636 - 2672
Main Author Lim, Meng Fai
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.11.2012
Subjects
Galois cohomology
Global fields
Poitou–Tate duality
Pontryagin dual
18E30
Pontryagin dual
11R34
11R23
11S25
Galois cohomology
Poitou–Tate duality
Global fields
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Summary:In this paper, we are interested in the Poitou–Tate duality in Galois cohomology. We will formulate and prove a theorem for a nice class of modules (with a continuous Galois action) over a pro-p ring. The theorem will comprise of the Tate local duality, Poitou–Tate duality and the Poitou–Tateʼs exact sequence.
ISSN:0022-314X
1096-1658
DOI:10.1016/j.jnt.2012.05.007