Toric varieties, monoid schemes and $cdh$ descent

By Guillermo Cortiñas, Christian Haesemeyer, M. Walker, Charles A. Weibel. 2011

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We give conditions for the Mayer-Vietoris property to hold for the algebraic K-theory of blow-up squares of toric varieties in any characteristic, 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 for monoid schemes many notions from classical algebraic geometry, such as separated and proper maps.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/66d7624f5937ddce0898efc43bf2b43fc00ba9e6