Abstract
Let K be a CDVF of mixed characteristic (0,p), whose residue field admits a finite p-basis. Assuming that K is weakly unramified over its canonical subfield, we establish an equivalence between prismatic de Rham crystals on the absolute prismatic site of O_K and nearly de Rham representations of G_K. Both sides are classified by certain enhanced connections, with the Galois side described via a decompleted p-adic Riemann–Hilbert correspondence. In this talk, I will focus on representations, with C-coefficients, where C is the completed algebraic closure of K.