Abstract
We show that if X is a toric scheme over a regular commutative ring k then the direct limit of the K-groups of X taken over any infinite sequence of nontrivial dilations is homotopy invariant. This theorem was previously known for regular commutative rings containing a field. The affine case of our result was conjectured by Gubeladze. We prove analogous results when k is replaced by an appropriate K-regular, not necessarily commutative k-algebra.
Cortiñas’ research was supported by Conicet and partially supported by grants UBACyT 20021030100481BA, PIP 112-201101-00800CO, PICT 2013-0454, and MTM2015-65764-C3-1-P (Feder funds).
Walker’s research was partially supported by a grant from the Simons Foundation (#318705).
Walker’s research was partially supported by a grant from the Simons Foundation (#318705).
Weibel’s research was supported by NSA and NSF grants.
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Acknowledgements
This article is part of a collection of papers published in honour of Antonio Campillo’s 65th birthday. The first named author is very grateful to him for all his help over many years; the authors dedicate this paper to him.
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Cortiñas, G., Haesemeyer, C., Walker, M.E., Weibel, C.A. (2018). The K-Theory of Toric Schemes Over Regular Rings of Mixed Characteristic. In: Greuel, GM., Narváez Macarro, L., Xambó-Descamps, S. (eds) Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics. Springer, Cham. https://doi.org/10.1007/978-3-319-96827-8_19
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