In algebraic geometry, the moduli stack of rank-n vector bundles Vectn is the stack parametrizing vector bundles (or locally free sheaves) of rank n over some reasonable spaces.
It is a smooth algebraic stack of the negative dimension
[1] Moreover, viewing a rank-n vector bundle as a principal
-bundle, Vectn is isomorphic to the classifying stack
For the base category, let C be the category of schemes of finite type over a fixed field k. Then
is a prestack over C. That it is a stack over C is precisely the statement "vector bundles have the descent property".
over U is the category of rank-n vector bundles over U where every morphism is an isomorphism (i.e., each fiber of p is a groupoid).
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