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arXiv · 2002.01538

Witt vectors with coefficients and characteristic polynomials over non-commutative rings

Emanuele Dotto·Achim Krause·Thomas Nikolaus·Irakli Patchkoria
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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 $\chi_f \in W(R)$. This element is a non-commutative analogue of the classical characteristic polynomial and we show that it has similar properties. The assignment $f \mapsto \chi_f$ induces an isomorphism between a suitable completion of cyclic K-theory and W(R).

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BibTeXRIS

Emanuele Dotto, Achim Krause, Thomas Nikolaus, Irakli Patchkoria. 2020-02-04. Witt vectors with coefficients and characteristic polynomials over non-commutative rings. https://arxiv.org/abs/2002.01538

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