Non-commutative Hodge-to-de Rham Degeneration via the Method of Deligne-Illusie

Abstract

1 Linear algebra. 6 1.1 Recollection on homology of small categories. . . . . . . . . . 6 1.2 Example: simplicial vector spaces. . . . . . . . . . . . . . . . 8 1.3 Effectively finite simplicial objects. . . . . . . . . . . . . . . . 11 1.4 Fibrations and cofibrations. . . . . . . . . . . . . . . . . . . . 13 1.5 Versions of the cyclic category. . . . . . . . . . . . . . . . . . 16 1.6 Cyclic homology and periodicity. . . . . . . . . . . . . . . . . 18 1.7 Homological effects of the p-fold coverings. . . . . . . . . . . . 22 1.8 Relation to group homology. . . . . . . . . . . . . . . . . . . . 25