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In mathematics, the formalism of ''B''-admissible representations provides constructions of full Tannakian subcategories of the category of representations of a group ''G'' on finite-dimensional vector spaces over a given field ''E''. In this theory, ''B'' is chosen to be a so-called (''E'', ''G'')-regular ring, i.e. an ''E''-algebra with an ''E''-linear action of ''G'' satisfying certain conditions given below. This theory is most prominently used in ''p''-adic Hodge theory to define important subcategories of ''p''-adic Galois representations of the absolute Galois group of local and global fields. ==(''E'', ''G'')-rings and the functor ''D''== Let ''G'' be a group and ''E'' a field. Let Rep(''G'') denote a non-trivial strictly full subcategory of the Tannakian category of ''E''-linear representations of ''G'' on finite-dimensional vector spaces over ''E'' stable under subobjects, quotient objects, direct sums, tensor products, and duals.〔Of course, the entire category of representations can be taken, but this generality allows, for example if ''G'' and ''E'' have topologies, to only consider continuous representations.〕 An (''E'', ''G'')-ring is a commutative ring ''B'' that is an ''E''-algebra with an ''E''-linear action of ''G''. Let ''F'' = ''BG'' be the ''G''-invariants of ''B''. The covariant functor ''DB'' : Rep(''G'') → Mod''F'' defined by : is ''E''-linear (Mod''F'' denotes the category of ''F''-modules). The inclusion of ''DB''(V) in ''B'' ⊗''EV'' induces a homomorphism : called the comparison morphism.〔A contravariant formalism can also be defined. In this case, the functor used is , the ''G''-invariant linear homomorphisms from ''V'' to ''B''.〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「B-admissible representation」の詳細全文を読む スポンサード リンク
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