A^1-homotopy theory and contractible varieties: a survey

Abstract

We survey some topics in ${\mathbb{A}}^1$-homotopy theory. Our main goal is to highlight the interplay between ${\mathbb{A}}^1$-homotopy theory and affine algebraic geometry, focusing on the varieties that are "contractible" from various standpoints.

arXiv comment52 pages; comments welcome!

References in corpus (4)

• The rationality problem for fields of invariants under linear algebraic groups (with special regards to the Brauer group)
• Suspensions of homology spheres
• On exotic algebraic structures on affine spaces
• The boundary motive: definition and basic properties