Tagged Questions

3
votes
1answer
78 views

vector bundles on the affine line over a PID

Let $R$ be a PID. Is every finitely generated projective $R[T]$-module free? In other words, is every vector bundle on $\mathbb{A}^1_R$ trivial? For $R=k[X]$ this is true by the Theorem of ...
5
votes
0answers
75 views

When is the pushforward / direct image of a reflexive sheaf locally free?

I have seen a number of theorems that guarantee the direct image of a reflexive sheaf to be reflexive again, or for the direct image of a locally-free sheaf to be locally free again. This makes me ...