Finitely Presented Spectrum

An fp-spectrum, or finitely presented spectrum in the cohomological convention, is a bounded-below -complete spectrum whose mod- cohomology is finitely presented as a module over the Steenrod algebra. It need not be a finite spectrum. Its fp-type is at most when is finite in total for a finite -local spectrum of chromatic type . Equivalently, the condition holds for every such . Finite in total means finitely many nonzero groups, each finite. Exact fp-type two means fp-type at most two but not at most one. The Hahn-Wilson conjecture compares this cohomological condition with finite constructions from truncated Brown-Peterson spectra.