Affine representability results in A1-homotopy theory, I: Vector bundles

Abstract

We establish a general "affine representability" result in A(double-struck)1-homotopy theory over a general base. We apply this result to obtain representability results for vector bundles in A(double-struck)1-homotopy theory. Our results simplify and significantly generalize Morel's A(double-struck)1-representability theorem for vector bundles.