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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