Suslin's cancellation conjecture in the smooth case

TL;DR

This paper proves Suslin's cancellation conjecture for smooth affine varieties over algebraically closed fields, showing that stably isomorphic vector bundles of a certain rank are actually isomorphic under specific conditions.

Contribution

It confirms Suslin's conjecture in the smooth case when d! is invertible in the base field, advancing understanding of vector bundle isomorphisms.

Findings

Stably isomorphic vector bundles of rank d-1 are isomorphic on smooth affine d-folds.

The result holds when d! is invertible in the base field.

Answers an old conjecture of Suslin in algebraic geometry.

Abstract

We prove that stably isomorphic vector bundles of rank d-1 on a smooth affine d-fold X over an algebraically closed field k are indeed isomorphic, provided d! is invertible in k. This answers an old conjecture of Suslin.