Kisin’s recipe Sample Clauses

Kisin’s recipe. As with the other two recipes, we split into the ir- reducible and reducible case. First assume ρGp is irreducible, where Kisin sets µn,m(ρ) = 1 if ρI ~ ω ⊗ ω(n+1) 0 and µn,m(ρ) = 0 otherwise. 0 ωp(n+1) ! Next we continue with the reducible case, Kisin sets µn,m(ρ) = 0 unless ρGp ~ ω ⊗ ωn+1µλ ∗ 0 µλ' for λ, λ′ ∈ F× in which case we set µn,m(ρ) = 1 except in the following cases: (1) If n = p — 1, λ = λ′ and ∗ is peu ramifi´ee (including the trivial case), then µn,m(ρ) = 2. (2) If n = 0, λ = λ′ and ∗ is tr`es ramifi´ee, then µn,m(ρ) = 0. (3) If n = p — 2, and ρGp is semi-simple, then µp−2,m(ρ) = 2 if λ λ′. If n = p — 2, and ρGp is semi-simple and λ = λ′, Kisin does not define µp−2,m(ρ) explicitly, but defines it to be the Xxxxxxx–Xxxxxx multiplicity obtained by taking τ trivial and k = p in his conjecture ( [Kis09a, Conjecture 1.1.5]). Kisin notes that global considerations suggest the integer µp−2,m(ρ) to be 2 if λ = λ′. However, in [San14, Theorem 1], this multiplicity has been computed explicitly. We will