Selecta Mathematica

, Volume 23, Issue 2, pp 1235–1247 | Cite as

Analogues of Gersten’s conjecture for singular schemes

  • Amalendu Krishna
  • Matthew Morrow


We formulate analogues, for Noetherian local \({\mathbb {Q}}\)-algebras which are not necessarily regular, of the injectivity part of Gersten’s conjecture in algebraic K-theory and prove them in various cases. Our results suggest that the algebraic K-theory of such a ring should be detected by combining the algebraic K-theory of both its regular locus and the infinitesimal thickenings of its singular locus.


Gersten’s conjecture Algebraic K-theory Singular schemes 

Mathematics Subject Classification

Primary 19E08 Secondary 14B05 



The second author would like to thank the Tata Institute of Fundamental Research for its hospitality during a visit in November 2012. The authors would like to thank the anonymous referee for carefully reading the paper and suggesting many improvements.


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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.MumbaiIndia
  2. 2.BonnGermany

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