Motivic de Rham-Witt complex

Amalendu Krishna, Jinhyun Park

Published 2015-04-30Version 1

We show that additive higher Chow groups in the Milnor range on smooth varieties over a perfect field of characteristic $p \not = 2$ induce a Zariski sheaf of pro-differential graded algebras, whose Milnor range is isomorphic to the Zariski sheaf of the big de Rham-Witt complexes of Hesselholt and Madsen. When $p>2$, the Zariski hypercohomology of the $p$-typical part of the sheaf arising from additive higher Chow groups computes the crystalline cohomology of smooth proper varieties. This revisits the 1970s results of S. Bloch and L. Illusie on crystalline cohomology.