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arXiv · 1703.07881

The $K$-theory of toric schemes over regular rings of mixed characteristic

Guillermo Cortiñas·Christian Haesemeyer·Mark E. Walker·Charles Weibel
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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.

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Guillermo Cortiñas, Christian Haesemeyer, Mark E. Walker, Charles Weibel. 2017-03-22. The $K$-theory of toric schemes over regular rings of mixed characteristic. https://arxiv.org/abs/1703.07881

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