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- W4221147861 abstract "For the cyclic group $C_2$ we give a complete description of the derived category of perfect complexes of modules over the constant Mackey ring $underline{mathbb{Z}/ell}$, for $ell$ a prime. This is fairly simple for $ell$ odd, but for $ell=2$ depends on a new splitting theorem. As corollaries of the splitting theorem we compute the associated Picard group and the Balmer spectrum for compact objects in the derived category, and we obtain a complete classification of finite modules over the $C_2$-equivariant Eilenberg--MacLane spectrum $Hunderline{mathbb{Z}/2}$. We also use the splitting theorem to give new and illuminating proofs of some facts about $RO(C_2)$-graded Bredon cohomology, namely Kronholm's freeness theorem and the structure theorem of C. May." @default.
- W4221147861 created "2022-04-03" @default.
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- W4221147861 date "2022-03-10" @default.
- W4221147861 modified "2023-10-14" @default.
- W4221147861 title "Equivariant $underline{mathbb{Z}/ell}$-modules for the cyclic group $C_2$" @default.
- W4221147861 doi "https://doi.org/10.48550/arxiv.2203.05287" @default.
- W4221147861 hasPublicationYear "2022" @default.
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