Vector bundles on contractible smooth schemes

Vector bundles on contractible smooth schemes

We discuss algebraic vector bundles on smooth k-schemes X contractible from the standpoint of A-homotopy theory; when k = C, the smooth manifolds X(C) are contractible as topological spaces. The integral algebraic K-theory and integral motivic cohomology of such schemes are that of Spec k. One might hope that furthermore, and in analogy with the classification of topological vector bundles on m...

On unipotent quotients and some A-contractible smooth schemes

We study quotients of quasi-affine schemes by unipotent groups over fields of characteristic 0. To do this, we introduce a notion of stability which allows us to characterize exactly when a principal bundle quotient exists and, together with a cohomological vanishing criterion, to characterize whether or not the resulting quasi-affine quotient scheme is affine. We completely analyze the case of...

Unipotent groups and some A1-contractible smooth schemes

Vanishing of sections of vector bundles on 0-dimensional schemes

Here we give conditions and examples for the surjectivity or injectivity of the restriction map H(X,F ) → H(Z, F |Z), where X is a projective variety, F is a vector bundle on X and Z is a “general” 0-dimensional subscheme of X, Z union of general

The Elementary Transformation of Vector Bundles on Regular Schemes

We give a generalized definition of an elementary transformation of vector bundles on regular schemes by using Maximal Cohen-Macaulay sheaves on divisors. This definition is a natural extension of that given by Maruyama, and has a connection with that given by Sumihiro. By this elementary transformation, we can construct, up to tensoring line bundles, all vector bundles from trivial bundles on ...