Abstract
We extend the results of Emerton on the ordinary part functor to the category of the smooth representations over a general commutative ring R, of a general reductive p-adic group G (rational points of a reductive connected group over a local non-archimedean field F of residual characteristic p). In Emerton’s work, the characteristic of F is 0, R is a complete artinian local \(\mathbb{Z}_{p}\) -algebra having a finite residual field, and the representations are admissible. We show:
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