Some computations in the heart of the homotopy t-structure on logarithmic motives

Abstract

In this note we will illustrate a method for computing the ${\pi }_0$ of the effective log motive of a smooth and proper variety over a perfect field $k$ and show that it is ${\mathbf{A}}^1$-invariant. We will apply this to compute the first homotopy groups of ${\mathbf{P}}^1$ to show that the stripping functor from log motivic sheaves to (usual) Nisnevich sheaves with transfers is fully faithful.

Accepted in J. Pure Appl. Algebra