2022/03/10 by Daniel Dugger, Dugger, Daniel, Christy Hazel +3
Mathematics · #Advanced Operator Algebra Research #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2203.05287
openalex publication_date 2022/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For the cyclic group C2 we give a complete description of the derived category of perfect complexes of modules over the constant Mackey ring \underlineℤ/ℓ, for ℓ a prime. This is fairly simple for ℓ odd, but for ℓ=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 C2-equivariant Eilenberg--MacLane spectrum H\underlineℤ/2. We also use the splitting theorem to give new and illuminating proofs of some facts about RO(C2)-graded Bredon cohomology, namely Kronholm's freeness theorem and the structure theorem of C. May.