Abstract
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.
Funding source: Conicet
Funding source: Feder
Award Identifier / Grant number: PIP 112-200801-00900
Funding source: Feder
Award Identifier / Grant number: MTM2007-64704
Funding source: Feder
Award Identifier / Grant number: UBACyT W386
Funding source: NSF
Award Identifier / Grant number: DMS-0966821
Funding source: NSF
Award Identifier / Grant number: DMS-0601666
Funding source: NSA
The authors would like to thank the referee for a careful reading, for suggesting the notion of a monoid poset and for the current proof of Lemma 5.5.
© 2015 by De Gruyter