We want to study vector bundles over rigid analytic varieties. Classical
results suggest that homotopy theory might be a good tool to classify
vector bundles up to isomorphism. Following this idea, the first
question is: Are isomorphism classes of vector bundles invariant under
"homotopy"? In our case, this question translates into a commutative
algebra question about projective modules: A variant of the Bass-Quillen
conjecture.
In the talk I will give a short introduction into rigid analytic
varieties and affinoid algebras. I will explain the conjecture, give a
picture of its geometric meaning and tell you what is known. I will not
speak about abstract homotopy theory. This is work in progress.