Homology, Homotopy and Applications
Volume 19 (2017)
Relative Tate objects and boundary maps in the $K$-theory of coherent sheaves
Pages: 341 – 369
We investigate the properties of relative analogues of admissible Ind, Pro, and elementary Tate objects for pairs of exact categories, and give criteria for those categories to be abelian. A relative index map is introduced, and as an application we deduce a description for boundary morphisms in the $K$-theory of coherent sheaves on Noetherian schemes.
Tate object, ind-pro object, boundary map
2010 Mathematics Subject Classification