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arXiv · 1310.6262

Cohomological finiteness conditions for Mackey and cohomological Mackey functors

Simon St John-Green
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Abstract

We study cohomological finiteness conditions for groups associated to Mackey and cohomological Mackey functors, proving that the cohomological dimension associated to cohomological Mackey functors is always equal to the $\mathcal{F}$-cohomological dimension, and characterising the conditions Mackey-$\mathrm{FP}_n$ and cohomological Mackey-$\mathrm{FP}_n$. We show that all finiteness conditions for cohomological Mackey functors are unchanged when considering only the family of $p$-subgroups, and we characterise cohomological Mackey-$\mathrm{FP}_n$ conditions over the finite field $\mathbb{F}_p$.

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Simon St John-Green. 2013-12-05. Cohomological finiteness conditions for Mackey and cohomological Mackey functors. https://arxiv.org/abs/1310.6262

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