A splitting result for the algebraic K-theory of projective toric schemes

Details A splitting result for the algebraic K-theory of projective toric schemes A splitting result for the algebraic K-theory of projective toric schemes

2010-07-29

arxiv.org/abs/1007.5231v3

Mathematics

K-Theory and Homology

29 pages. V2: updated bibliography, typos corrected; v3: final version, to appear in Journal of Homotopy and Related Structure

Scientific paper

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.

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