Dotto, Emanuele, Krause, Achim, Nikolaus, Thomas and Patchkoria, Irakli (2022) Witt vectors with coefficients and characteristic polynomials over non-commutative rings. Compositio Mathematica, 158 (2). pp. 366-408. doi:10.1112/S0010437X22007254 ISSN 0010-437X.

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Abstract

For a not-necessarily commutative ring R we define an abelian group W(R;M) of Witt vectors with coefficients in an R-bimodule M. These groups generalize the usual big Witt vectors of commutative rings and we prove that they have analogous formal properties and structure. One main result is that W(R):=W(R;R) is Morita invariant in R. For an R-linear endomorphism f of a finitely generated projective R-module we define a characteristic element χf∈W(R). This element is a non-commutative analogue of the classical characteristic polynomial and we show that it has similar properties. The assignment f↦χf induces an isomorphism between a suitable completion of cyclic K-theory K
cyc0(R) and W(R).

Item Type:	Journal Article
Alternative Title:
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH):	Commutative rings, K-theory, Noncommutative algebras, Algebra
Journal or Publication Title:	Compositio Mathematica
Publisher:	Cambridge University Press
ISSN:	0010-437X
Official Date:	February 2022
Dates:	Date Event February 2022 Published 26 April 2022 Available 20 July 2021 Accepted
Volume:	158
Number:	2
Page Range:	pp. 366-408
DOI:	10.1112/S0010437X22007254
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access (Creative Commons)
Date of first compliant deposit:	21 July 2021
Date of first compliant Open Access:	22 July 2021
RIOXX Funder/Project Grant:	Project/Grant ID RIOXX Funder Name Funder ID EXC 2044 390685587 [DFG] Deutsche Forschungsgemeinschaft http://dx.doi.org/10.13039/501100001659 UNSPECIFIED [DFG] Deutsche Forschungsgemeinschaft http://dx.doi.org/10.13039/501100001659 UNSPECIFIED Hausdorff Center for Mathematics UNSPECIFIED
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