2021/02/10 by Chetan Balwe, Balwe, Chetan, Amit Hogadi +3
Mathematics · #14F42 #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #K-Theory and Homology (math.KT) #math.AG #math.AT #math.KT #msc:14F42
paper · pdf · doi:10.48550/arxiv.2102.05344
v4: 17 pages, final version before page proofs, accepted for publication in Journal of Algebraic Geometry
arxiv created 2021/08/19 · arxiv updated 2021/08/20
We show that \mathbb A1-connectedness of a large class of varieties over a field k can be characterized as the condition that their generic point can be connected to a k-rational point using (not necessarily naive) \mathbb A1-homotopies. We also show that symmetric powers of \mathbb A1-connected varieties (over an arbitrary field), as well as smooth proper models of them (over an algebraically closed field of characteristic 0), are \mathbb A1-connected. As an application of these results, we show that the standard norm varieties over a field k of characteristic 0 become \mathbb A1-connected (and consequently, universally R-trivial) after base change to an algebraic closure of k.