p-ADIC PERIODS AND DERIVED DE RHAM COHOMOLOGY.

The article considers another construction of the p-adic period map using the de Rham cohomology of Illusie and de Jong's alterations in a bid to understand the Riemann-Hilbert correspondence in this setting. Information on the derived de Rham algebra is provided, as well as the integer rings. It cites the projective system of commutative dg algebras. Also included are information on a reinterpretation of Colmez's theorem and derived de Rham algebra in logarithmic setting.