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Results tagged with connections
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user 11682
Ehresmann connections; covariant derivatives; connections on vector bundles, principal bundles, ∞-bundles, submersions, bundle gerbes; holonomy and higher holonomy; parallel transport; torsion; curvature. See also the tags [principal-bundles], [vector-bundles], [gerbes], [curvature], [geodesics], [characteristic-classes], [torsion].
24
votes
The algebraic version of Riemann-Hilbert correspondence
As the previous answer points out you have to consider local systems for a finer topology than the Zariski topology. It is natural to consider the étale topology. The category of étale local systems o …
- 1,446
5
votes
Pullback of a connection
Connections on the trivial bundle are of the form $d+\Omega$, where $\Omega$ is a matrix of $1$-forms. It is enough to take the matrix obtained by pulling back each form individually. … Finally, the uniqueness ensures that you can glue these local connections together to get a global solution. …
- 4,008
4
votes
Katz's proof of Cartier's (descent) theorem
If you are looking for a modern treatment, my advice would be to look at Michael Groechning's very nice proof here:
Moduli of flat connections in positive characteristic
Mathematical Research Letters …
- 4,008