Filtration by weight on the de Rham cohomology of a projective non singular curve over an ultrametric complete field (Q1904089)

We consider a nonsingular projective curve over a complete ultrametric field. We endow its first de Rham cohomology space with a filtration, called the weight filtration. It is a three steps, decreasing functorial filtration that has the following properties: 1. It is isomorphic to its Poincaré dual; 2. It is transversal to the Hodge filtration; and 3. It extends the conjugate analytic filtration. The construction of this filtration uses various rigid cohomology spaces associated to the reduction of the curve.