Galois cohomology Sample Clauses

Galois cohomology. We write OL,Σ for the subring of L comprising elements of L which are integral at all places outside those which lie above a place in Σ. Let LΣ be the maximum algebraic extension of L in Qc unramified outside Σ, and write GL,Σ for Gal(LΣ/L). Define Zp(1) to be the inverse limit ←lim− µpn of the groups of pn-th roots of unity in Qc, and note that this is a continuous Zp[GL,Σ]-module. Writing wv for a place in LΣ which lies above a v ∈ Σ and Gwv for the corresponding decomposition group, there is a ‘localisation’ morphism M C•(GL,Σ, Zp(1)) → C•(Gwv , Zp(1)).
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Related to Galois cohomology

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