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Niveau spectral sequences on singular schemes and failure of generalized Gersten conjecture


Author: Paul Balmer
Journal: Proc. Amer. Math. Soc. 137 (2009), 99-106
MSC (2000): Primary 19E08, 19D35, 18E30
DOI: https://doi.org/10.1090/S0002-9939-08-09496-3
Published electronically: July 10, 2008
MathSciNet review: 2439430
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Abstract: We construct a new local-global spectral sequence for Thomason's non-connective $ K$-theory, generalizing the Quillen spectral sequence to possibly non-regular schemes. Our spectral sequence starts at the $ E_1$-page where it displays Gersten-type complexes. It agrees with Thomason's hypercohomology spectral sequence exactly when these Gersten-type complexes are locally exact, a condition which fails for general singular schemes, as we indicate.


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Additional Information

Paul Balmer
Affiliation: Department of Mathematics, Box 951555, University of California, Los Angeles, California 90095-1555
Email: balmer@math.ucla.edu

DOI: https://doi.org/10.1090/S0002-9939-08-09496-3
Keywords: Spectral sequence, $K$-theory, singular schemes
Received by editor(s): September 17, 2007
Received by editor(s) in revised form: January 9, 2008
Published electronically: July 10, 2008
Additional Notes: The author’s research was supported by NSF grant 0654397.
Communicated by: Paul Goerss
Article copyright: © Copyright 2008 Paul Balmer

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