2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/105104We introduce a version of the Cartier isomorphism for de Rham cohomology valid for associative, not necessarily commutative algebras over a field of positive characteristic. Using this, we imitate the well-known argument of P. Deligne and L. Iluusie and prove, in some cases, a conjecture of M. Kontsevich which claims that the Hodge-to-de Rham, a.k.a. Hochschild-to-cyclic spectral sequence degenerates.53 pages, LaTeX2eAlgebraic GeometryK-Theory and Homologytext