The K-Theory of Toric Schemes Over Regular Rings of Mixed Characteristic

G. Cortiñas (), C. Haesemeyer (), M. E. Walker () and C. A. Weibel ()
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G. Cortiñas: Universidad de Buenos Aires, Department of Matemática-Inst. Santaló, FCEyN
C. Haesemeyer: University of Melbourne, School of Mathematics and Statistics
M. E. Walker: University of Nebraska – Lincoln, Department of Mathematics
C. A. Weibel: Rutgers University, Department of Mathematics

A chapter in Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics, 2018, pp 455-479 from Springer

Abstract: 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.

Keywords: Commutative Regular Rings; Gubeladze; Monoid Scheme; Finite Krull Dimension; Cyclotomic Trace (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-96827-8_19

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DOI: 10.1007/978-3-319-96827-8_19

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