Marc Levine. K-theory and motivic cohomology of schemes. Preprint, available at http: //www.math.uiuc.edu/K-theory, February 1999. Home/Search Document Not in Database Summary Related Articles Check |
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Geometric Models For Algebraic K-Theory - Grayson, Walker (1999) (Correct)
....a result might be possible was suggested by E. Friedlander. More generally, if Y is equidimensional) the spaces K t ( Delta ffl ; Y ) t = 0; dimY; form a sort of filtration of K 0 (Y ) given by codimension of support, which may be related to the filtrations considered in [2] and [6]. One consequence of realizing these various K theory spaces as mapping complexes of varieties is that we may then take other topological realizations of the same basic construction. For example, consider the case Y = SpecC . Our construction will yield a weak equivalence (for X a regular complex ....
Marc Levine. K-theory and motivic cohomology of schemes. Preprint, available at http: //www.math.uiuc.edu/K-theory, February 1999.
K-Theory Of Semi-Local Rings With Finite Coefficients And.. - Kahn (1999) (Correct)
....a by product, we get that (1.3) degenerates completely and canonically for fields under the conditions of theorem 1. What we need as a crucial tool is the existence of a product structure on this spectral sequence. A construction of this product structure was performed only recently by Marc Levine [33] and also by Friedlander Suslin (in preparation) thanks to the latter s reinterpretation of the Bloch Lichtenbaum spectral sequence. To the best of our efforts, we haven t been able to find an argument avoiding it. This explains the long delay between the first version of this paper and its ....
....over a field (Friedlander Suslin, in preparation) and even regular schemes over a regular base of dimension 1 (Levine [32] This also gave another, direct, construction of the Rognes Weibel variant with finite coefficients. Finally, it allowed Friedlander Suslin (in preparation) and Levine [33] to provide these spectral sequences with a product structure. The product structure on (3.1) and the easier existence of transfers allow us to play the same game as in [26] and [28] using the anti Chern classes to kill all differentials of the spectral sequence and show that the E1 filtration on ....
M. Levine K-theory and motivic cohomology of schemes, preprint, 1999.
On The Cyclotomic Trace Map. . . - Østvær (1999) (Correct)
....for n odd. 2) If F is real, then n is injective for n 1; 5 mod 8 and split injective for n 7 mod 8. Proof. The slick way to prove this is to employ the extended integral Bloch Lichtenbaum spectral sequence for the number ring and for the local number ring as constructed by Levine in [Le]. That spectral sequence is natural, and after tensoring with the two adic integers we nd commutative diagrams K 2n 1 (RF ; Z 2 ) ## ## K 2n 1 (OF ; Z 2 ) ## H 1 et (RF ; Z 2 (n) ## H 1 et (OF ; Z 2 (n) and K 2n (RF ; Z 2 ) ## ## K 2n (OF ; Z 2 ) ## H 2 et (RF ; Z 2 (n 1) ## ....
M. Levine, K{theory and motivic cohomology of schemes, http://www.math.uiuc.edu/Ktheory /0336/ (1999).
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