2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/166167The Kontsevich-Soibelman solution of the cyclic version of Deligne's conjecture and the formality of the operad of little discs on a cylinder provide us with a natural homotopy calculus structure on the pair (C^*(A), C_*(A)) ``Hochschild cochains + Hochschild chains'' of an associative algebra A. We show that for an arbitrary smooth algebraic variety X with the structure sheaf O_X the sheaf (C^*(O_X), C_*(O_X)) of homotopy calculi is formal. This result was announced in paper [29] by the second and the third author.To Mikhail Olshanetsky on the occasion of his 70th birthdayK-Theory and HomologyQuantum Algebratext