The zeroth P^1-stable homotopy sheaf of a motivic space

Abstract

We establish a kind of "degree zero Freudenthal Gm-suspension theorem" in motivic homotopy theory. From this we deduce results about the conservativity of the P^1-stabilization functor. In order to establish these results, we show how to compute certain pullbacks in the cohomology of a strictly homotopy invariant sheaf in terms of the Rost--Schmid complex. This establishes the main conjecture of [BY18], which easily implies the aforementioned results.

v3: final version v2: minor corrections

References in corpus (5)

• Higher Topos Theory
• The six operations in equivariant motivic homotopy theory
• Nilpotence and descent in equivariant stable homotopy theory
• The Simplicial EHP Sequence in A1-Algebraic Topology
• Towards conservativity of ${\mathbb{G}}_m$-stabilization