Toric varieties, monoid schemes and cdh descent

Authors

Guillermo Cortiñas, Universidad de Buenos AiresFollow
C. Haesemeyer, University of California - Los AngelesFollow
Mark E. Walker, University of Nebraska - LincolnFollow
Charles Weibel, Rutgers UniversityFollow

Date of this Version

2015

Citation

J. reine angew. Math. 698 (2015), 1–54

Journal für die reine und angewandte Mathematik

DOI 10.1515/ crelle-2012-0123

Comments

© De Gruyter 2015. Used by permission.

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.