$v_1$-periodic motivic homotopy over prime fields

Abstract

We compute the motivic stable homotopy groups of a variant of the connective image-of-J spectrum over prime fields of characteristic not two. Together with the analogous computation over algebraically closed fields, this yields information about v1periodic motivic stable homotopy groups over arbitrary base fields of characteristic not two. Contents1. Introduction 1 2. Background 5 3. Coefficient rings of HZ{2 n 10 4. Coefficient rings of kq 12 5. Coefficient rings of L over prime fields 15 Appendix A. Figures 20 References 29