De Rham–Witt sheaves via algebraic cycles

De Rham–Witt sheaves via algebraic cycles

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

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Veröffentlicht in:Compositio mathematica 2021-10, Vol.157 (10), p.2089-2132
Hauptverfasser: Krishna, Amalendu, Park, Jinhyun
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Sheaves
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Zusammenfassung:We show that the additive higher Chow groups of regular schemes over a field induce a Zariski sheaf of pro-differential graded algebras, the Milnor range of which 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.
ISSN:0010-437X
1570-5846
DOI:10.1112/S0010437X21007478