A class of 2-local finite spectra which admit a [formula omitted]-self-map

Abstract

At the prime 2, Behrens, Hill, Hopkins and Mahowald showed that M2(1,4) admits a 32-periodic v2-self-map. More recently, in joint work with Mahowald, we showed that A1 also admits a 32-periodic v2-self-map. This leads to the question of whether there exists a finite 2-local complex with periodicity less than 32. We answer this question in the affirmative by producing a class of finite 2-local spectra Z˜ all of which admit a 1-periodic v2-self-map.