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The slice spectral sequence for singular schemes and applications
- Source :
- Ann. K-Th. 3 (2018) 657-708
- Publication Year :
- 2016
-
Abstract
- We examine the slice spectral sequence for the cohomology of singular schemes with respect to various motivic T-spectra, especially the motivic cobordism spectrum. When the base field k admits resolution of singularities and X is a scheme of finite type over k, we show that Voevodsky's slice filtration leads to a spectral sequence for MGL(X) whose terms are the motivic cohomology groups of X defined using the cdh-hypercohomology. As a consequence, we establish an isomorphism between certain geometric parts of the motivic cobordism and motivic cohomology of X. A similar spectral sequence for the connective K-theory leads to a cycle class map from the motivic cohomology to the homotopy invariant K-theory of X. We show that this cycle class map is injective for projective schemes. We also deduce applications to the torsion in the motivic cohomology of singular schemes.<br />Comment: 37 pages. Final version. To appear in Annals of K-theory
- Subjects :
- Mathematics - Algebraic Geometry
Mathematics - K-Theory and Homology
Subjects
Details
- Database :
- arXiv
- Journal :
- Ann. K-Th. 3 (2018) 657-708
- Publication Type :
- Report
- Accession number :
- edsarx.1606.05810
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.2140/akt.2018.3.657