DOI: 10.1515/crelle-2023-0084 ISSN: 0075-4102

𝔸1-connected components and characterisation of 𝔸2

Utsav Choudhury, Biman Roy
  • Applied Mathematics
  • General Mathematics


In this article, we prove that any

A 1 \mathbb{A}^{1}
-contractible smooth complex surface is isomorphic as a variety to
C 2 \mathbb{C}^{2}
. We show that the
A 1 \mathbb{A}^{1}
-connected component of a variety 𝑋 contains the information about
A 1 \mathbb{A}^{1}
’s in 𝑋.