\mathbbA¹-connected components of blow-up of threefolds fibered over a surface

2020/09/20 by Rakesh Pawar, Pawar, Rakesh
Mathematics · #14F35 #14F42 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric and Algebraic Topology #K-Theory and Homology (math.KT) #math.AG #math.AT #math.KT #msc:14F35 #msc:14F42

paper · pdf · doi:10.48550/arxiv.2009.09424

19 pages, major restructuring/changes in exposition after initial journal report

openalex publication_date 2020/09/20 · arxiv created 2022/02/23 · arxiv updated 2022/02/24 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

Over a perfect field, we determine the sheaf of \mathbbA¹-connected components of a class of threefolds given by the Blow-up of a variety admitting a ℙ¹-fibration over either an \mathbbA¹-rigid or a non-uniruled surface, along a smooth curve. As a consequence, we verify that the sheaf of \mathbbA¹-connected components for such varieties is \mathbbA¹-invariant.

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