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Convergence of the Motivic Adams Spectral Sequence

Published online by Cambridge University Press:  11 April 2011

P. Hu ,
I. Kriz  and
K. Ormsby
P. Hu
Affiliation:
Department of Mathematics, Wayne State University, U.S.A., po@math.wayne.edu
I. Kriz
Affiliation:
Department of Mathematics, University of Michigan, U.S.A., ikriz@umich.edu
K. Ormsby
Affiliation:
Department of Mathematics, MIT, U.S.A., ormsby@math.mit.edu
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Abstract

We prove convergence of the motivic Adams spectral sequence to completions at p and η under suitable conditions. We also discuss further conditions under which η can be removed from the statement.

Keywords

motivic Adams spectral sequencemotivic homotopy theory.
Type
Research Article
Information
Journal of K-Theory , Volume 7 , Issue 3 , June 2011 , pp. 573 - 596
Copyright
Copyright © ISOPP 2011

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References

1.Adams, J.F.: Stable homotopy and generalised homology, Chicago Lectures in Mathematics, University of Chicago Press, 1973Google Scholar
2.Arason, J.: Cohomologische invarianten quadratischer Formen, J. Algebra 36 (1975) 448–491CrossRefGoogle Scholar
3.Bousfield, A.K., Kan, D.M.: Homotopy limits, completions and localizations, Lecture Notes in Mathematics 304, Springer Verlag, 1972Google Scholar
4.Brown, E.H., Cohen, R.L.: The Adams spectral sequence of Ω2S 3 and Brown-Gitler spectra, in: Algebraic Topology and Algebraic K-theory, Browder, W., ed., Annals of Math. Studies 113, Princeton Univ. Press, Princeton, NJ, 1987, pp. 101–125Google Scholar
5.Bousfield, A.K.: The localization of spectra with respect to homology, Topology 18 (1979) 257–281CrossRefGoogle Scholar
6.Dugger, D., Isaksen, D.: The motivic Adams spectral sequence, Geom. Topol. 14/2 (2010) 967–1014Google Scholar
7.Dugger, D., Isaksen, D.: Motivic cell structures, Algebr. Geom. Topol. 5 (2005) 615–652Google Scholar
8.Hill, M.: Ext and the motivic Steenrod algebra over ℝ, J. Pure and Appl. Alg. 215/5 (2011) 715–727Google Scholar
9.Hu, P., Kriz, I., Ormsby, K.: Remarks on motivic homotopy theory over algebraically closed fields, J. K-Theory 7 (2011) 55–89CrossRefGoogle Scholar
10.Hu, P., Kriz, I., Ormsby, K.: Equivariant and real motivic stable homotopy theory, K-theory archive 952Google Scholar
11.Lam, T. Y.. Introduction to quadratic forms over fields, Graduate Studies in Mathematics 67, American Mathematical Society, Providence, RI, 2005.Google Scholar
12.Milnor, J.: Algebraic K-theory and quadratic forms, Invent. Math. 9 (1969/1970) 318–344CrossRefGoogle Scholar
13.Morel, F.: On the motivic stable π0 of the sphere spectrum, Axiomatic, Enriched and Motivic Homotopy Theory, pp. 219–260, 2004 Kluwer Academic PublishersGoogle Scholar
14.Morel, F.: An introduction to -homotopy theory, Contemporary developments in algebraic K-theory, ICTP Lect. Notes, XV (2004) 357–441Google Scholar
15.Østvær, P.A., Röndigs, O.: Rigidity in motivic homotopy theory, Math. Ann. 341 (2008) 651–675Google Scholar
16.Ormsby, K.: Motivic invariants of p-adic fields, J. K-Theory 7 (2011), to appearGoogle Scholar
17.Serre, J.P.: Galois Cohomology, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2002Google Scholar
18.Voevodsky, V.: On Motivic Cohomology with ℤ/ℓ coefficients, arXiv:0805.4430Google Scholar
19.Voevodsky, V.: Motivic cohomology with Z/2-coefficients, Publ. Math. Inst. Hautes Études Sci. 98 (2003) 59–104Google Scholar
20.Voevodsky, V.: Reduced power operations in motivic cohomology, Publ. Math. Inst. Hautes Études Sci. 98 (2003) 1–57Google Scholar
21.Voevodsky, V.: Motivic Eilberg-Maclane spaces, Publ. Math. IHES 112 (2010) 1–99Google Scholar