科研之友
微信
新浪微博
Facebook
分享链接
摘要
We give a cohomological classification of vector bundles of rank 2 on a smooth affine threefold over an algebraically closed field having characteristic unequal to 2. As a consequence we deduce that cancellation, holds for rank 2 vector bundles on such varieties. The proofs of these results involve three main ingredients. First, we give a description of the first nonstable A(1)-homotopy sheaf of the symplectic group. Second, these computations can be used in concert with E Morel%26apos;s A(1)-homotopy classification of vector bundles on smooth affine schemes and obstruction theoretic techniques (stemming from a version of the Postnikov tower in A(1)-homotopy theory) to reduce the classification results to cohomology vanishing statements. Third, we prove the required vanishing statements.
- 出版日期2014-11-1
