Homology, Homotopy and Applications

Volume 19 (2017)

Number 1

Relative Tate objects and boundary maps in the $K$-theory of coherent sheaves

Pages: 341 – 369

DOI: http://dx.doi.org/10.4310/HHA.2017.v19.n1.a17


Oliver Braunling (Department of Mathematics, Universität Freiburg, Germany)

Michael Groechenig (Department of Mathematics, Imperial College London, United Kingdom)

Jesse Wolfson (Department of Mathematics, University of Chicago, Illinois, U.S.A.)


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

19D99, 22B99

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