Resumen de Crystallinity of rigid flat connections revisited

Hélène Esnault, Michael Groechenig

• We generalise a theorem on the existence of Frobenius isocrystal and FontaineLaffaille module structures on rigid flat connections to the non-proper setting. The proof is based on a new strategy of a point-set topological flavour, which allows us to produce a purely p-adic statement and thereby to avoid the classical Simpson correspondence.