volume 34 issue 4 pages 613-683

Eilenberg-Moore spectral sequence and Hodge cohomology of classifying stacks

Publication typeJournal Article
Publication date2025-05-12
scimago Q1
SJR1.846
CiteScore2.8
Impact factor
ISSN10563911, 15347486
Abstract

Let G G be a smooth connected reductive group over a field k k and Γ \Gamma be a central subgroup of G G . We construct Eilenberg-Moore-type spectral sequences converging to the Hodge and de Rham cohomology of B ( G / Γ ) B(G/\Gamma ) . As an application, building upon work of Toda and using Totaro’s inequality, we show that for all m 0 m\geq 0 the Hodge and de Rham cohomology algebras of the classifying stacks B P G L 4 m + 2 B\mathrm {PGL}_{4m+2} and B P S O 4 m + 2 B\mathrm {PSO}_{4m+2} over F 2 \mathbb {F}_2 are isomorphic to the singular F 2 \mathbb {F}_2 -cohomology of the classifying space of the corresponding Lie group. From this we obtain a full description of H > 0 ( G L 4 m + 2 , Sym j ( p g l 4 m + 2 ) ) H^{>0}(\mathrm {GL}_{4m+2}, \operatorname {Sym}^j(\mathfrak {pgl}_{4m+2}^\vee )) and H > 0 ( S O 4 m + 2 , Sym j ( p s o 4 m + 2 ) ) H^{>0}(\mathrm {SO}_{4m+2}, \operatorname {Sym}^j(\mathfrak {pso}_{4m+2}^\vee )) over F 2 \mathbb F_2 .

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Kubrak D. et al. Eilenberg-Moore spectral sequence and Hodge cohomology of classifying stacks // Journal of Algebraic Geometry. 2025. Vol. 34. No. 4. pp. 613-683.
GOST all authors (up to 50) Copy
Kubrak D., Scavia F. Eilenberg-Moore spectral sequence and Hodge cohomology of classifying stacks // Journal of Algebraic Geometry. 2025. Vol. 34. No. 4. pp. 613-683.
RIS |
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RIS Copy
TY - JOUR
DO - 10.1090/jag/846
UR - https://www.ams.org/jag/0000-000-00/S1056-3911-2025-00846-0/
TI - Eilenberg-Moore spectral sequence and Hodge cohomology of classifying stacks
T2 - Journal of Algebraic Geometry
AU - Kubrak, Dimitry
AU - Scavia, Federico
PY - 2025
DA - 2025/05/12
PB - American Mathematical Society
SP - 613-683
IS - 4
VL - 34
SN - 1056-3911
SN - 1534-7486
ER -
BibTex |
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@article{2025_Kubrak,
author = {Dimitry Kubrak and Federico Scavia},
title = {Eilenberg-Moore spectral sequence and Hodge cohomology of classifying stacks},
journal = {Journal of Algebraic Geometry},
year = {2025},
volume = {34},
publisher = {American Mathematical Society},
month = {may},
url = {https://www.ams.org/jag/0000-000-00/S1056-3911-2025-00846-0/},
number = {4},
pages = {613--683},
doi = {10.1090/jag/846}
}
MLA
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Kubrak, Dimitry, et al. “Eilenberg-Moore spectral sequence and Hodge cohomology of classifying stacks.” Journal of Algebraic Geometry, vol. 34, no. 4, May. 2025, pp. 613-683. https://www.ams.org/jag/0000-000-00/S1056-3911-2025-00846-0/.