The Generalized De Rham-Witt Complex and Congruence Differential Equations

Abstract

The De Rham-Witt complex is a powerful instrument for studying the crystalline cohomology of a smooth projective variety over a perfect field of positive characteristic. In [9] the De Rham-Witt complex is constructed for schemes on which some prime number p is zero. Here in section 2 we construct on every scheme X on which 2 is invertible the generalized De Rham-Witt complex W Ω X this is a Zariski sheaf of anti-commutative differential graded algebras with the additional structures and properties described in (2.1)–(2.6). Section 3 gives the (obvious) definition of the relative generalized De Rham-Witt complex W Ω X/S for f: X → S a morphism of schemes over Z[1/2].KeywordsUnit RootWitt VectorPerfect FieldCrystalline CohomologyWitt ComplexThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.