  We construct a co-t-structure on the derived category of coherent sheaves on
the nilpotent cone, as well as on the derived category of coherent sheaves on
any parabolic Springer resolution. These structures are employed to show that
the push-forwards of the "exotic parity objects" (considered in
\cite{achar-hardesty-riche}), along the (classical) Springer resolution, give
indecomposable objects inside the coheart of the co-t-structure on $\cN$.We
also demonstrate how the various parabolic co-t-structures can be related by
introducing an analogue to the usual translation functors.
  Additional applications include a proof of the scheme-theoretic formulation
of Humphreys conjecture on support varieties of tilting modules in type $A$ for
$p>h$, as well as a verification of the conjecture in arbitrary type, (for
$p>h$), over a large class of orbits, which includes all Richardson orbits. We
also obtain new information regarding the structure of certain $p$-canonical
cells and thick-tensor-ideals of tilting modules.
