Surjectivity of the etale excision map for homotopy invariant framed presheaves

TL;DR

This paper proves the surjectivity of the etale excision map for homotopy invariant framed presheaves over any infinite ground field, extending previous results that had restrictions on the field's characteristic.

Contribution

It establishes the surjectivity of the etale excision property for A1-invariant stable framed presheaves over any infinite field, removing earlier characteristic restrictions.

Findings

Surjectivity of etale excision holds over any infinite ground field.

Previous restrictions on the characteristic of the ground field are now removed.

The results unify and extend prior work on framed presheaves and motivic homotopy theory.

Abstract

The category of framed correspondences Fr_*(k), framed presheaves and framed sheaves were invented by Voevodsky in his unpublished notes [17]. Based on the notes [17] a new approach to the classical Morel--Voevodsky motivic stable homotopy theory was developed by G.Garkusha and I.Panin in [8]. The purpose of this paper is to prove Theorem 1.1 stating that if the ground field k is infinite, then the surjectivity of the etale excision property is true for any A1-invariant stable radditive framed presheaf of Abelian groups F. The injectivity of the etale excision was proved in [9]. The surjectivity of the etale excision was proved in [9] if the ground field is infinite of characteristic not 2. In this preprint the surjectivity of the etale excision is proved in the case of any infinite ground field. As explained in the introduction to [8] all the results of [9], [1], [10] and [8] are true now automatically without any restrictions on the characteristic of the ground field.