2017/03/17 by Anand Sawant, Sawant, Anand
Mathematics · #14F42 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #K-Theory and Homology (math.KT) #math.AG #math.KT #msc:14F42
paper · pdf · doi:10.48550/arxiv.1703.05935
10 pages; to appear in the Proceedings of International Colloquium on K-theory 2016, Tata Institute of Fundamental Research, Mumbai, India
arxiv created 2017/03/17 · openalex publication_date 2017/03/17 · arxiv updated 2017/03/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that the triviality of sections of the sheaf of A1-chain connected components of a space over finitely generated separable field extensions of the base field is not sufficient to ensure the triviality of the sheaf of its A1-chain connected components, contrary to the situation with genuine A1-connected components. As a consequence, we show that there exists an A1-connected scheme for which the Morel-Voevodsky singular construction is not A1-local.