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

Balmer, Paul

doi:10.1090/S0002-9939-08-09496-3

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

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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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