Witt vectors with coefficients and characteristic polynomials over non-commutative rings. Issue 2 (26th February 2022) - Dotto, Emanuele; Krause, Achim; Nikolaus, Thomas; Patchkoria, Irakli
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 χ _f 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 χ _f induces an isomorphism between a suitable completion of cyclic K -theory K_0^cyc(R) and W(R) .