Automatically assigned DDC number: 51266

Manually assigned DDC number: 51266

Number of references: 16

Title: K-Theory And Motivic Cohomology Of Schemes

Author:

Subject: Marc Levine K-Theory And Motivic Cohomology Of Schemes

Description: . We examine some of the basic properties satisfied by Bloch's cycle complexes for quasi-projective varieties over a field, and extend some of them to the cycle complex of a scheme of finite type over a regular dimension one base. We also give an extension to the simplicial spectra in the niveau tower of the cosimplicial scheme Delta X . As applications, we show that the AtiyahHirzebruch spectral sequence from motivic cohomology to K-theory admits a multiplicative structure, has Adams operations, and maps to a similar spectral sequence from 'etale cohomology to 'etale K-theory. 0. Introduction In [36], we have described an extension of the cycle complexes z q (X; ) of Bloch to schemes X of finite type over a regular one-dimensional base B. We also considered the niveau tower : : : G (qGamma1) (X; Gamma) ! G (q) (X; Gamma) ! : : : ! G (d) (X; Gamma) G(X); dim X d; where G (q) (X; Gamma) is the simplicial spectrum p 7! G (q) (X; p), and G (q) (X; p), roughly speaking, is de...

Contributor: The Pennsylvania State University CiteSeer Archives

Publisher: unknown

Date: 1999-02-27

Format: ps

Identifier: http://citeseer.ist.psu.edu/259873.html

Source: http://www.math.uiuc.edu/K-theory/0336/mot.ps.gz

Language: en

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