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Counterexamples to Hochschild-Kostant-Rosenberg in characteristic p

Part of: Commutative algebra: Homological methods (Co)homology theory Homological methods Higher algebraic $K$-theory

Published online by Cambridge University Press:  22 June 2021

Benjamin Antieau ,
Bhargav Bhatt  and
Akhil Mathew
Benjamin Antieau
Affiliation:
Department of Mathematics, Northwestern University, Evanston, IL60208; E-mail: antieau@northwestern.edu
Bhargav Bhatt
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, MI48109; E-mail: bhattb@umich.edu
Akhil Mathew
Affiliation:
Department of Mathematics, University of Chicago, Chicago, IL60637; E-mail: amathew@math.uchicago.edu

Abstract

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We give counterexamples to the degeneration of the Hochschild-Kostant-Rosenberg spectral sequence in characteristic p, both in the untwisted and twisted settings. We also prove that the de Rham-HP and crystalline-TP spectral sequences need not degenerate.

MSC classification

Primary: 13D03: (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.)
Secondary: 14F40: de Rham cohomology 16E40: (Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.) 19D55: $K$-theory and homology; cyclic homology and cohomology
Type
Algebraic and Complex Geometry
Information
Forum of Mathematics, Sigma , Volume 9 , 2021 , e49
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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