On torsion spaces

Abstract

The purpose of this note is to construct examples of compact torsion objects of ${\cal SH}(F)$ of every $p$-level over an arbitrary field of characteristic different from $p$. We adapt the approach of Mitchell to the algebraic situation. We show that the respective level is determined by the action of the $v_m$-elements on the $MGL$-motive, and also prove the refinement which permits to distinguish isotropic Morava points of the Balmer spectrum of ${\cal SH}(F)$.