Author:
Barnes David,Greenlees J. P. C.,Kędziorek Magdalena
Abstract
AbstractEquipping a non-equivariant topological $$\text {E}_\infty $$
E
∞
-operad with the trivial G-action gives an operad in G-spaces. For a G-spectrum, being an algebra over this operad does not provide any multiplicative norm maps on homotopy groups. Algebras over this operad are called naïve-commutative ring G-spectra. In this paper we take $$G=SO(2)$$
G
=
S
O
(
2
)
and we show that commutative algebras in the algebraic model for rational SO(2)-spectra model rational naïve-commutative ring SO(2)-spectra. In particular, this applies to show that the SO(2)-equivariant cohomology associated to an elliptic curve C of Greenlees (Topology 44(6):1213–1279, 2005) is represented by an $$\text {E}_\infty $$
E
∞
-ring spectrum. Moreover, the category of modules over that $$\text {E}_\infty $$
E
∞
-ring spectrum is equivalent to the derived category of sheaves over the elliptic curve C with the Zariski torsion point topology.
Publisher
Springer Science and Business Media LLC
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