Cohomology on the centric orbit category of a fusion system
Volume 269 / 2025
Fundamenta Mathematicae 269 (2025), 187-199
MSC: Primary 20E25; Secondary 55R35, 20J06, 20D20, 55R40
DOI: 10.4064/fm240612-2-2
Published online: 13 March 2025
Abstract
We study the higher derived limits of mod $p$ cohomology on the centric orbit category of a saturated fusion system on a finite $p$-group. It is an open problem whether all such higher limits vanish. This is known in many cases, including for fusion systems realized by a finite group and for many classes of fusion systems which are not so realized. We prove that the higher limits of $H^j$ vanish provided $j \leq p-2$, by showing that the same is true for the contravariant part of a simple Mackey composition factor of $H^j$ under the same conditions.
