Equivariant real cycle class map and Witt-sheaf cohomology of classifying spaces

Lorenzo Mantovani; Ákos K. Matszangosz; Matthias Wendt

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arXiv · 2602.20367

Equivariant real cycle class map and Witt-sheaf cohomology of classifying spaces

Lorenzo Mantovani·Ákos K. Matszangosz·Matthias Wendt

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Abstract

In this paper, we study equivariant real cycle class maps for group actions on real schemes, with a view toward Witt-sheaf characteristic classes. The cycle class maps take values in singular cohomology of the real points of the quotient stack, which are identified with the homotopy fixed-points of complex conjugation on the complex points. This provides a strong relation between Witt-sheaf cohomology of the geometric classifying space of a real algebraic group and the singular cohomology of the classifying spaces of its strong real forms, which we discuss in a number of examples. As a sample application, we compute the number of Witt-sheaf cohomological invariants of spin groups over the reals.

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BibTeX RIS

Lorenzo Mantovani, Ákos K. Matszangosz, Matthias Wendt. 2026-02-23. Equivariant real cycle class map and Witt-sheaf cohomology of classifying spaces. https://arxiv.org/abs/2602.20367

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