Definition of the filtration Sample Clauses

Definition of the filtration. Suppose χ is a continuous char- acter GK → Fˆ. Recall from [Ser79, Ch. IV,§3] that we have a decreasing K filtration on GK by closed subgroups Gu given by the upper numbering on K GK for u < X. Xxxxxx also that Gu = GK for u “ —1, that for —1 c u “ 0 K G K we have Gu = IK, the inertia subgroup of GK, and that Ťuą0 u = PK, the wild inertia subgroup of GK. For s < R, we will define an increasing filtration Fils on H1(GK, Fp(χ)) by the rule K p K p K p FilsH1(G , F (χ)) := č ker ´H1(G , F (χ)) —r—es→ H1(Gu , F (χ))¯ . uąs´1 ď We will, furthermore, define FilăsH1(GK, Fp(χ)) := FiltH1(GK, Fp(χ)) tăs and define the associated grading by K p FilăsH1(G
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