A splitting theorem for connected moravaK-theories

Abstract

LetX be a connected, locally finite spectrum and letk(n) (n>-1) denote the (−1)-connected cover of then-th MoravaK-Theory associated to the primep.k(n) is aBP-module spectrum with π*(k(n)) ≅ ℤp[υn] where |vn| = 2(pn-1). We prove the following splitting theorem: Thek(n)*-torsion ofk(n)* (X) is already annihilated byvne (e≥1) if and only ifk(n)ΛX is homotopy equivalent to a wedge of spectrak(n) andrk(n) (0≤r≤e-1) whererk(n) denotes ther-th Postnikov factor ofk(n). Moreover we investigate splitting conditions forrk(n)ΛX.