K-Theory of non-linear projective toric varieties

Details K-Theory of non-linear projective toric varieties K-Theory of non-linear projective toric varieties

2005-08-23

arxiv.org/abs/math/0508431v2

Forum Mathematicum 21 no. 1 (2009), pp. 67-100

Mathematics

K-Theory and Homology

v2: Final version, to appear in "Forum Mathematicum". Minor changes only, added more cross-referencing and references for tori

Scientific paper

10.1515/FORUM.2009.004

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.

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