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

摘要

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.