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

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- by Paul Balmer
- Proc. Amer. Math. Soc.
**137**(2009), 99-106 - DOI: https://doi.org/10.1090/S0002-9939-08-09496-3
- Published electronically: July 10, 2008

## 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.## References

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## Bibliographic Information

**Paul Balmer**- Affiliation: Department of Mathematics, Box 951555, University of California, Los Angeles, California 90095-1555
- MR Author ID: 652084
- Email: balmer@math.ucla.edu
- 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
- © Copyright 2008 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
- MathSciNet review: 2439430