2024/01/18 by Geoff Vooys, Vooys, Geoff
Mathematics · #14F08 #14F43 #14M17 #18N10 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Primary 14A30 #Secondary 18G15
paper · pdf · doi:10.48550/arxiv.2401.10174
openalex publication_date 2024/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 DGb(X; ℚℓ) ≃ DGb(Perv(X;ℚℓ)) where ℓ 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.