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

MARK E. WALKER; GUILLERMO CORTIÑAS; CHARLES A. WEIBEL; CHRISTIAN HAESEMEYER

Singularities, algebraic geometry, commutative algebra and related topics

springer

Año: 2018; p. 455 - 479

We show that if $X$ is a toric scheme over aregular commutative ring $k$then the direct limit of the $K$-groups of $X$ taken over anyinfinite sequence of nontrivial dilations is homotopy invariant.This theorem was previously known for regular commutative ringscontaining a field. The affinecase of our result was conjectured by Gubeladze.We prove analogous results when $k$ is replaced by anappropriate $K$-regular, not necessarily commutative $k$-algebra.