Submission: 2012, Nov 15
Let G be a finite group of exponent m and let k be a field of characteristic prime to m, containing the m-th roots of unity. For any Rost cycle module M over k, we construct exact sequences detecting the unramified elements in Serre's group of invariants of G with values in M in terms of "residue" morphisms associated to pairs (D,g), where D runs through the subgroups of G and g runs through the homomorphisms \mu_m \to G whose image centralises D. This allows us to recover results of Bogomolov and Peyre on the unramified cohomology of fields of invariants of G, and to generalise them.
2010 Mathematics Subject Classification:
Keywords and Phrases: Classifying spaces, cycle modules, cohomological invariants.
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