Abstract
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.
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Acknowledgments
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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Krishna, A., Morrow, M. Analogues of Gersten’s conjecture for singular schemes. Sel. Math. New Ser. 23, 1235–1247 (2017). https://doi.org/10.1007/s00029-016-0256-8
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DOI: https://doi.org/10.1007/s00029-016-0256-8