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De Rham–Witt sheaves via algebraic cycles

Part of: $K$-theory in geometry Arithmetic rings and other special rings Cycles and subschemes (Co)homology theory

Published online by Cambridge University Press:  19 August 2021

Amalendu Krishna  and
Jinhyun Park
Amalendu Krishna
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, 1 Homi Bhabha Road, Colaba, Mumbai, [email protected]
Jinhyun Park
Affiliation:
Department of Mathematical Sciences, KAIST, 291 Daehak-ro Yuseong-gu, Daejeon, 34141, Republic of Korea (South) [email protected], [email protected]
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Abstract

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.

Keywords

algebraic cyclesde Rham–Witt complexcrystalline cohomology

MSC classification

Primary: 14C25: Algebraic cycles
Secondary: 13F35: Witt vectors and related rings 14F30: $p$-adic cohomology, crystalline cohomology 19E15: Algebraic cycles and motivic cohomology
Type
Research Article
Information
Compositio Mathematica , Volume 157 , Issue 10 , October 2021 , pp. 2089 - 2132
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Copyright
© 2021 The Author(s). The publishing rights in this article are licensed to Foundation Compositio Mathematica under an exclusive licence

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Footnotes

With an appendix by Kay Rülling

J.P. was partially supported by the National Research Foundation of Korea (NRF; grant numbers 2015R1A2A2A01004120 and 2018R1A2B6002287) funded by the Korean government (MSIP), and TJ Park Junior Faculty Fellowship funded by POSCO TJ Park Foundation.

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