Arithmetic Geometry

For any smooth projective curve over a finite field, we construct the p-adic analytic moduli stack of isocrystals and study its geometry. This is the crystalline analogue of the moduli of integrable connections. Notably, even though it is a...

We use Teichmüller theory to construct a new geometric model for the classifying space of the mapping class group of a three-dimensional handlebody. Two consequences are obtained: (i) Chan-Galatius-Payne have shown that the homology of Kontsevich's...