Perverse homotopy heart and MW-modules

TL;DR

This paper computes the perverse delta-homotopy heart of the motivic stable homotopy category over a base scheme, introducing homological and cohomological Milnor-Witt cycle modules and establishing duality results.

Contribution

It introduces homological and cohomological Milnor-Witt cycle modules and constructs a homotopy-invariant Rost-Schmid cycle complex for the motivic stable homotopy category.

Findings

Computed the perverse delta-homotopy heart over a base scheme.

Defined homological and cohomological Milnor-Witt cycle modules.

Established duality results in the smooth case.

Abstract

We compute the perverse delta-homotopy heart of the motivic stable homotopy category over a base scheme with a dimension function delta, rationally or after inverting the exponential characteristic in the equicharacteristic case. In order to do that, we define the notion of homological Milnor-Witt cycle modules and construct a homotopy-invariant Rost-Schmid cycle complex. Moreover, we define the category of cohomological Milnor-Witt cycle modules and show a duality result in the smooth case.