PERVERSE COHERENT SHEAVES IN GOOD CHARACTERISTIC 23
Theorem 6.3. The functor real :
DbPCohG×Gm
(N )


DbCohG×Gm
(N ) is an
equivalence of categories.
Proof. By Lemma 5.5(2), we have
Homd(ON
M(λ),A(λ)) = 0 for all
d 0. It follows that if X
PCohG×Gm
(N ) is a λ-quasicostandard object,
then
Homd(ON
M(λ),X) = 0. By Lemma 5.4, we have a surjective map
ON M(λ) A(λ). Thus, part (2) of Definition 3.5 holds. By Lemma 5.1, the
Serre–Grothendieck duality functor exchanges standard and costandard objects, so
part (1) of Definition 3.5 follows from part (2). By Theorem 3.15, the desired
equivalence holds.
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Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803,
U.S.A.
E-mail address: pramod@math.lsu.edu
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