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

Emanuele Dotto, Achim Krause, Thomas Nikolaus, Irakli Patchkoria* (Corresponding Author)

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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).
Original languageEnglish
Pages (from-to)366-408
Number of pages43
JournalCompositio Mathematica
Issue number2
Early online date26 Apr 2022
Publication statusPublished - 26 Apr 2022


  • Witt vectors
  • characteristic polynomial
  • trace


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