**abstract:**
_{work} in progress_{} with V. Srinivas.

Over the complex numbers, an étally simply connected, not necessarily proper manifold does not have any non-trivial regular singular connection. We can't prove the analog in characteristic $p>0$, which would be a non-proper version of Gieseker conjecture. Simply connected manifolds in characteristic $p>0$ have more constraints than in characteristic $0$. We show a few features and can understand the situation in one or two examples.

Wed 18 Dec, 9:15 - 10:15, Aula Dini

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