Twists of Kisin modules and Galois representations Sample Clauses

Twists of Kisin modules and Galois representations. We now wish to relate twisting our Galois extensions to twists of Kisin modules. First recall we have a functor TS from Kisin modules to G∞-modules. By the exactness of TS we obtain a commutative diagram: Ext1(M1, M2) Ext1(M′1, M′2) Ext1(TS(M1), TS(M2)) ∼ Ext1(TS(M1′ ), TS(M′2)) Figure 1. Commutative diagram of extension spaces. where the isomorphism on the bottom is obtained by twisting any extension by TS(M′).
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