Abstract
AbstractWe prove that the derived parabolic induction functor, defined on the unbounded derived category of smooth mod p representations of a p-adic reductive group, admits a left adjoint $$\textrm{L}(U,-)$$
L
(
U
,
-
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. We study the cohomology functors $$\textrm{H}^i\circ \textrm{L}(U,-)$$
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i
∘
L
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U
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in some detail and deduce that $$\textrm{L}(U,-)$$
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preserves bounded complexes and global admissibility in the sense of Schneider–Sorensen. Using $$\textrm{L}(U,-)$$
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we define a derived Satake homomorphism and prove that it encodes the mod p Satake homomorphisms defined explicitly by Herzig.
Funder
Westfälische Wilhelms-Universität Münster
Publisher
Springer Science and Business Media LLC