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.

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

Cited by in corpus (3)

• A splitting result for the algebraic K-theory of projective toric schemes
• A cohomological interpretation of Brion's formula
• Finite domination and Novikov homology over strongly ${\mathbb{Z}}^2$-graded rings