2016/01/07 by Aravind Asok, Asok, Aravind
Mathematics · #14E08 #14F42 #19E15 #19G12 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #math.AG #math.AT #math.KT #msc:14E08 #msc:14F42 #msc:19E15 #msc:19G12
paper · pdf · doi:10.48550/arxiv.1601.01615
12 pages, Comments welcome!
arxiv created 2016/01/07 · openalex publication_date 2016/01/07 · arxiv updated 2016/01/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the relationship between several notions of connectedness arising in \mathbb A1-homotopy theory of smooth schemes over a field k: \mathbb A1-connectedness, stable \mathbb A1-connectedness and motivic connectedness, and we discuss the relationship between these notations and rationality properties of algebraic varieties. Motivically connected smooth proper k-varieties are precisely those with universally trivial CH0. We show that stable \mathbb A1-connectedness coincides with motivic connectedness, under suitable hypotheses on k. Then, we observe that there exist stably \mathbb A1-connected smooth proper varieties over the field of complex numbers that are not \mathbb A1-connected.