A splitting result for the algebraic K-theory of projective toric schemes
arXiv:1007.5231 · doi:10.1007/s40062-012-0003-6
Abstract
Suppose X is a projective toric scheme defined over a commutative ring R equipped with an ample line bundle L. We prove that its K-theory has k+1 direct summands K(R) where k is minimal among non-negative integers such that the twisted line bundle L(-k-1) is not acyclic. In fact, using a combinatorial description of quasi-coherent sheaves throughout we prove the result for a ring R which is either commutative, or else left noetherian.
29 pages. V2: updated bibliography, typos corrected; v3: final version, to appear in Journal of Homotopy and Related Structures