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On the Equivariant Derived Category of Perverse Sheaves (2401.10174v1)
Published 18 Jan 2024 in math.AG and math.CT
Abstract: 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 $D_Gb(X; \overline{\mathbb{Q}}{\ell}) \simeq D_Gb(\mathbf{Perv}(X;\overline{\mathbb{Q}}{\ell}))$ 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.
- P.“@ N.“@ Achar “Perverse sheaves and applications to representation theory” 258, Mathematical Surveys and Monographs American Mathematical Society, 2021 DOI: “url–https://doi.org/10.1090/surv/258
- J.“@ Adams, D.“@ Barbasch and D.“@ A.“@ Vogan “The Langlands classification and irreducible characters for real reductive groups” 104, Progress in Mathematics Birkhäuser Boston, Inc., Boston, MA, 1992, pp. xii+318 DOI: 10.1007/978-1-4612-0383-4
- A.A. Beilinson “On the derived category of perverse sheaves” In K𝐾Kitalic_K-theory, arithmetic and geometry (Moscow, 1984–1986) 1289, Lecture Notes in Math. Springer, Berlin, 1987, pp. 27–41 DOI: 10.1007/BFb0078365
- A.“@ Belinson, J.“@ Bernstein, P.“@ Deligne and O.“@ Gabber “Faisceaux pevers” In analyse et topologie sur les espace singuliers 100, Astérisque Soc. Math. France, 1982, pp. 5–171
- “Equivariant sheaves and functors” 1578, Lecture Notes in Mathematics Springer-Verlag, Berlin, 1994, pp. iv+139 DOI: 10.1007/BFb0073549
- “Arthur packets for p𝑝pitalic_p-adic groups by way of microlocal vanishing cycles of perverse sheaves, with examples” In Memoirs of the AMS, 2022
- “Proof of Vogan’s conjecture on Arthur packets for GLnsubscript𝐺𝐿𝑛\mathop{GL}_{n}start_BIGOP italic_G italic_L end_BIGOP start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT over p𝑝pitalic_p-adic fields” Available at https://arxiv.org/abs/2302.10300. Accessed January 12, 2024., 2023 arXiv:2302.10300 [math.RT]
- T.“@ Ekedahl “On the adic formalism” In The Grothendieck Festschrift, Vol. II 87, Progr. Math. Birkhäuser Boston, Boston, MA, 1990, pp. 197–218
- A.“@ Huber “Mixed perverse sheaves for schemes over number fields” In Compositio Math. 108.1, 1997, pp. 107–121 DOI: 10.1023/A:1000273606373
- “2-dimensional categories” Oxford University Press, Oxford, 2021, pp. xix+615 DOI: 10.1093/oso/9780198871378.001.0001
- G.“@ Lusztig “Cuspidal local systems and graded Hecke algebras. II” With errata for Part I [Inst. Hautes Études Sci. Publ. Math. No. 67 (1988), 145–202; MR0972345 (90e:22029)] In Representations of groups (Banff, AB, 1994) 16, CMS Conf. Proc. Amer. Math. Soc., Providence, RI, 1995, pp. 217–275
- “Geometric invariant theory” 34, Ergebnisse der Mathematik und ihrer Grenzgebiete [Results in Mathematics and Related Areas] Springer-Verlag, Berlin, 1982, pp. xii+220 DOI: 10.1007/978-3-642-96676-7
- M. Raynaud “Faisceaux amples sur les schemas en groupes et les espaces homogenes”, Lecture Notes in Mathematics Springer Berlin Heidelberg, 2006
- G.“@ Vooys “Categories of Pseudocones and Equivariant Descent” Available on the arXiv (identifier to be updated)., 2024