2015/04/03 by Garkusha, Grigory, Panin, Ivan · 2 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1504.00884
The category of framed correspondences Fr_*(k), framed presheaves and framed sheaves were invented by Voevodsky in his unpublished notes [12]. Based on the theory, framed motives are introduced and studied in [7]. The main aim of this paper is to prove that for any \mathbb A1-invariant quasi-stable radditive framed presheaf of Abelian groups \mathcal F, the associated Nisnevich sheaf \mathcal Fnis is \mathbb A1-invariant whenever the base field k is infinite of characteristic different from 2. Moreover, if the base field k is infinite perfect of characteristic different from 2, then every \mathbb A1-invariant quasi-stable Nisnevich framed sheaf of Abelian groups is strictly \mathbb A1-invariant and quasi-stable. Furthermore, the same statements are true in characteristic 2 if we also assume that the \mathbb A1-invariant quasi-stable radditive framed presheaf of Abelian groups \mathcal F is a presheaf of \mathbb Z[1/2]-modules. This result and the paper are inspired by Voevodsky's paper [13].