K-Theory of non-linear projective toric varieties
Abstract
By analogy with algebraic geometry, we define a category of non-linear sheaves (quasi-coherent homotopy-sheaves of topological spaces) on projective toric varieties and prove a splitting result for its algebraic K-theory, generalising earlier results for projective spaces. The splitting is expressed in terms of the number of interior lattice points of dilations of a polytope associated to the variety. The proof uses combinatorial and geometrical results on polytopal complexes. The same methods also give an elementary explicit calculation of the cohomology groups of a projective toric variety over any commutative ring.
Keywords
Cite
@article{arxiv.math/0508431,
title = {K-Theory of non-linear projective toric varieties},
author = {Thomas Huettemann},
journal= {arXiv preprint arXiv:math/0508431},
year = {2010}
}
Comments
v2: Final version, to appear in "Forum Mathematicum". Minor changes only, added more cross-referencing and references for toric geometry