On the Equivariant Derived Category of Perverse Sheaves
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914645339537408 |
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| author | Vooys, Geoff |
| author_facet | Vooys, Geoff |
| contents | In this paper we extend Beilinson's realization formalism for triangulated categories and filtered triangulated categories to a pseudofunctorial and pseudonatural setting. As a consequence we prove an equivariant version of Beilinson's Theorem: for any algebraic group $G$ over an algebraically closed field $K$ and for any $G$-variety $X$, there is an equivalence of categories $D_G^b(X; \overline{\mathbb{Q}}_{\ell}) \simeq D_G^b(\mathbf{Perv}(X;\overline{\mathbb{Q}}_{\ell}))$ where $\ell$ is an integer prime coprime to the characteristic of $K$. We also show that the equivariant analogues of the other non-$D$-module aspects of Beilinson's Theorem hold in the equivariant case. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_10174 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Equivariant Derived Category of Perverse Sheaves Vooys, Geoff Algebraic Geometry Category Theory Primary 14A30, 18N10, Secondary 18G15, 14F08, 14F43, 14M17 In this paper we extend Beilinson's realization formalism for triangulated categories and filtered triangulated categories to a pseudofunctorial and pseudonatural setting. As a consequence we prove an equivariant version of Beilinson's Theorem: for any algebraic group $G$ over an algebraically closed field $K$ and for any $G$-variety $X$, there is an equivalence of categories $D_G^b(X; \overline{\mathbb{Q}}_{\ell}) \simeq D_G^b(\mathbf{Perv}(X;\overline{\mathbb{Q}}_{\ell}))$ where $\ell$ is an integer prime coprime to the characteristic of $K$. We also show that the equivariant analogues of the other non-$D$-module aspects of Beilinson's Theorem hold in the equivariant case. |
| title | On the Equivariant Derived Category of Perverse Sheaves |
| topic | Algebraic Geometry Category Theory Primary 14A30, 18N10, Secondary 18G15, 14F08, 14F43, 14M17 |
| url | https://arxiv.org/abs/2401.10174 |