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\mathbbA1-homotopy type of \mathbbA2 ∖ \(0,0) \

2024/04/01 by Utsav Choudhury, Choudhury, Utsav, Biman Kumar Saha Roy +1
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Algebraic structures and combinatorial models #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.2404.01087

Abstract

In this article we prove that any \mathbbA1-connected smooth k-variety is \mathbbA1-uniruled for any algebraically closed field k. We establish that if a non empty open subscheme X of a smooth affine k-scheme is \mathbbA1-weakly equivalent to \mathbbA2k ∖ \(0,0) \, then X ≅ \mathbbA2k ∖ \(0,0) \ as k-varieties for any field k of characteristic 0.

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