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Is there a notion of connection on a principal bundle over an algebraic or geometric stack? By a geometric stack, I mean a stack over category of manifolds that is representable by a Lie groupoid; ...

Given a manifold, one can associate a stack over the category of manifolds, which is a differential geometric stack. This gives a functor $\text{Man}\rightarrow \text{D.Stacks}$. This is an embedding....

Let $G$ be a reductive group. A $2$-shifted $2$-form on the classifying stack $BG$ is by definition a a morphism of quasi-coherent complexes \begin{equation} \mathcal O_{BG}\rightarrow (\wedge^2 \...

$\DeclareMathOperator\GL{GL}\DeclareMathOperator\Gr{Gr}$This may all be well known, too vague, or stupid; my apologies. The Gauss map is defined by embedding your $k$-dimensional smooth scheme/...

Suppose we have a commutative diagram of Artin stacks $ \newcommand{\ra}[1]{\kern-1.5ex\xrightarrow{\ \ #1\ \ }\phantom{}\kern-1.5ex} \newcommand{\ras}[1]{\kern-1.5ex\xrightarrow{\ \ \smash{#1}\ \ }\...