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The Right Adjoint of the Parabolic Induction

  • Marie-France VignérasEmail author
Chapter
Part of the Progress in Mathematics book series (PM, volume 319)

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:

The smooth parabolic induction functor admits a right adjoint. The center-locally finite part of the smooth right adjoint is equal to the admissible right adjoint of the admissible parabolic induction functor when R is noetherian. The smooth and admissible parabolic induction functors are fully faithful when p is nilpotent in R.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Institut de Mathematiques de JussieuUniversité de Paris 7ParisFrance

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