Using methods developed by Franke in [K-theory Preprint Archives 139 (1996)], we
obtain algebraic classification results for modules over certain symmetric
ring spectra (S-algebras). In particular, for any symmetric ring spectrum
whose graded homotopy
ring
has graded global
homological dimension
and is concentrated in degrees divisible by some natural number
, we prove that the homotopy
category of
–modules
is equivalent to the derived category of the homotopy ring
.
This improves the Bousfield-Wolbert algebraic classification of isomorphism
classes of objects of the homotopy category of R-modules. The
main examples of ring spectra to which our result applies are the
–local real connective
–theory spectrum
, the Johnson–Wilson
spectrum
, and the truncated
Brown–Peterson spectrum
,
all for an odd prime
.
We also show that the equivalences for all these examples are exotic in the sense that
they do not come from a zigzag of Quillen equivalences.
Keywords
algebraic classification, model category, module spectrum,
symmetric ring spectrum, stable model category
