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Toric varieties, monoid schemes and $cdh$ descent (1106.1389v2)
Published 7 Jun 2011 in math.KT and math.AG
Abstract: 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.