Let
be a
-adic
reductive group. We determine the extensions between admissible smooth mod
representations
of
parabolically induced from supersingular representations of Levi subgroups of
,
in terms of extensions between representations of Levi subgroups of
and
parabolic induction. This proves for the most part a conjecture formulated
by the author in a previous article and gives some strong evidence for the
remaining part. In order to do so, we use the derived functors of the left and
right adjoints of the parabolic induction functor, both related to Emerton’s
-functor of
derived ordinary parts. We compute the latter on parabolically induced representations
of
by
pushing to their limits the methods initiated and expanded by the author in previous
articles.
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