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arXiv · 2003.12021

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

Tom Bachmann
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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.

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Tom Bachmann. 2020-03-26. The zeroth P^1-stable homotopy sheaf of a motivic space. https://doi.org/10.1017/s1474748021000396

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