Framed correspondences and the zeroth stable motivic homotopy group in odd characteristic

Abstract

We extend the results of G.~Garkusha and I.~Panin on framed motives of algebraic varieties [4] to the case of a finite base field, and extend the computation of the zeroth cohomology group $H^0(\mathbb{Z}F({\Delta }_k^{\bullet },{\mathbf{G}}_m^{\wedge n}))=K_n^{MW}$ by A.~Neshitov [8] to perfect fields $k$ of positive characteristic different from 2.

The section 3 is corrected and split in two sections with more details