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K-Theory of non-linear projective toric varieties | | Thomas Huettemann
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23 Aug 2005 | | Subject: | K-Theory and Homology; Algebraic Topology MSC-class: 19D10 (Primary), 55P99 57Q05 14M25 (Secondary) | math.KT math.AT | | 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. | | Source: | arXiv, math.KT/0508431 | | Services: | Forum | Review | PDF | Favorites | |
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