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

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Abstract

For a not-necessarily commutative ring we define an abelian group of Witt vectors with coefficients in an -bimodule. 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 is Morita invariant in. For an -linear endomorphism of a finitely generated projective -module we define a characteristic element. This element is a non-commutative analogue of the classical characteristic polynomial and we show that it has similar properties. The assignment induces an isomorphism between a suitable completion of cyclic -theory and.

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Dotto, E., Krause, A., Nikolaus, T., & Patchkoria, I. (2022). Witt vectors with coefficients and characteristic polynomials over non-commutative rings. Compositio Mathematica, 158(2), 366–408. https://doi.org/10.1112/S0010437X22007254

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