Date of this Version
J. reine angew. Math. 698 (2015), 1–54
Journal für die reine und angewandte Mathematik
DOI 10.1515/ crelle-2012-0123
We give conditions for the Mayer–Vietoris property to hold for the algebraic K-theory of blow-up squares of toric varieties and schemes, using the theory of monoid schemes. These conditions are used to relate algebraic K-theory to topological cyclic homology in characteristic p. To achieve our goals, we develop many notions for monoid schemes based on classical algebraic geometry, such as separated and proper maps and resolution of singularities.