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arXiv · 1007.5231

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

Thomas Huettemann
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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.

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Thomas Huettemann. 2011-09-16. A splitting result for the algebraic K-theory of projective toric schemes. https://doi.org/10.1007/s40062-012-0003-6

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