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Zbl 1062.14024
Lyubashenko, Volodymyr
Tensor products of categories of equivariant perverse sheaves. (English)
[J] Cah. Topologie Géom. Différ. Catégoriques 43, No. 1, 49-79 (2002). ISSN 0008-0004

Let $G,H$ be complex algebraic groups acting on complex quasi-projective varieties $X,Y$ respectively. The author considers the abelian categories $\text{Perv}_G(X)$ and $\text{Perv}_H(Y)$ of equivariant perverse sheaves as defined by {\it J. Bernstein} and {\it V. Lunts} [``Equivariant sheaves and functors'', Lect. Notes Math. 1578 (1994; Zbl 0808.14038)]. It is proved that the abstract tensor product of this categories is naturally equivalent to $\text{Perv}_{G\times H} (X\times Y)$ via the external product functor $$\boxtimes: \text{Perv}_G(X) \times \text{Perv}_H(Y) \to \text{Perv}_{G\times H} (X\times Y),$$ $$F\boxtimes E=pr^*_1 F\otimes pr_2^*E$$ which makes the target category into the Deligne tensor product. \par This extends a similar result of the author [Ukr. Math. J. 53, No.3, 354--367 (2001; Zbl 0996.14008)] to the equivariant setup.
[Olaf Teschke (Berlin)]

MSC 2000:: *14F05 Sheaves, etc.
18E30 Derived categories, etc.
14F43 Other algebro-geometric (co)homologies
55N91 Equivariant homology and cohomology

Citations: Zbl 0996.14008; Zbl 0808.14038

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