The eta-inverted sphere over the rationals

Abstract

We calculate the motivic stable homotopy groups of the two-complete sphere spectrum after inverting multiplication by the Hopf map eta over fields of cohomological dimension at most 2 with characteristic different from 2 (this includes the p-adic fields and the finite fields of odd characteristic) and the field of rational numbers; the ring structure is also determined.

24 pages, 6 figures, 4 tables. To appear in Algebraic and Geometric Topology

References in corpus (2)

• Two-complete stable motivic stems over finite fields
• The eta-inverted R-motivic sphere

Cited by in corpus (4)

• The homotopy groups of the η-periodic motivic sphere spectrum
• Algebraic Cobordism and Étale Cohomology
• $\mathbb{R}$-motivic $v_1$-periodic homotopy
• The motivic lambda algebra and motivic Hopf invariant one problem