Abstract
The category of rational SO(2)equivariant spectra
admits an algebraic model. That is, there is an
abelian category A(SO(2)) whose derived
category is equivalent to the homotopy
category of rational$SO(2)equivariant spectra.
An important question is: does this algebraic model capture the
smash product of spectra?
The category A(SO(2)) is known as Greenlees'
standard model, it is an abelian category
that has no projective objects and is constructed from
modules over a nonNoetherian ring.
As a consequence, the standard techniques for constructing a
monoidal model structure cannot be applied.
In this paper a monoidal model structure on
A(SO(2)) is constructed and the derived tensor product on the homotopy
category is shown to be compatible with the smash product of spectra.
The method used is related to techniques developed
by the author in earlier joint work with Roitzheim. That work
constructed a monoidal model structure on Franke's
exotic model for the K_(p)local stable homotopy category.
A monoidal Quillen equivalence
to a simpler monoidal model category that has
explicit generating sets is also given. Having monoidal model structures
on the two categories removes a serious obstruction to constructing a series
of monoidal Quillen equivalences between the algebraic model
and rational SO(2)equivariant spectra.
Original language  English 

Pages (fromto)  167192 
Number of pages  26 
Journal  Mathematical Proceedings of the Cambridge Philosophical Society 
Volume  161 
Early online date  11 Apr 2016 
DOIs  
Publication status  Published  01 Jul 2016 
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David Barnes
 School of Mathematics and Physics  Senior Lecturer
 Mathematical Sciences Research Centre
Person: Academic