de Rham-Witt sheaves via algebraic cycles

2015/04/30 by Krishna, Amalendu, Park, Jinhyun, Rülling, with an appendix by Kay
#13F35 #14C25 (Primary) #14F30 #19E15 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.1504.08181

Abstract

We show that the additive higher Chow groups of regular schemes over a field induce a Zariski sheaf of pro-differential graded algebras, whose Milnor range is isomorphic to the Zariski sheaf of big de Rham-Witt complexes. This provides an explicit cycle-theoretic description of the big de Rham-Witt sheaves. Several applications are derived.

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• Big de Rham-Witt cohomology: basic results