2018/10/08 by David Barnes, Barnes, David, J. P. C. Greenlees +3
Mathematics · #55N91 #55P42 #55P60 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1810.03632
openalex publication_date 2018/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Equipping a non-equivariant topological E_\∞-operad with the trivial\nG-action gives an operad in G-spaces. For a G-spectrum, being an algebra\nover this operad does not provide any multiplicative norm maps on homotopy\ngroups. Algebras over this operad are called na "ive-commutative ring\nG-spectra. In this paper we take G=SO(2) and we show that commutative\nalgebras in the algebraic model for rational SO(2)-spectra model rational\nna "ive-commutative ring SO(2)-spectra. In particular, this applies to show\nthat the SO(2)-equivariant cohomology associated to an elliptic curve C\nfrom previous work of the second author is represented by an E_\∞-ring\nspectrum. Moreover, the category of modules over that E_\∞-ring spectrum\nis equivalent to the derived category of sheaves over the elliptic curve C\nwith the Zariski torsion point topology.\n