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Tr. Mat. Inst. Steklova, 2004, Volume 246, Pages 106–115 (Mi tm148)  

This article is cited in 17 scientific papers (total in 17 papers)

On the Zero Slice of the Sphere Spectrum

V. A. Voevodskii

Institute for Advanced Study, School of Mathematics

Abstract: We prove the motivic analogue of the statement saying that the zero stable homotopy group of spheres is $\mathbf Z$. In topology, this is equivalent to the fact that the fiber of the obvious map from the sphere $S^n$ to the Eilenberg–MacLane space $K(\mathbf Z,n)$ is $(n+1)$-connected. We prove our motivic analogue by an explicit geometric investigation of a similar map in the motivic world. Since we use the model of the motivic Eilenberg–MacLane spaces based on the symmetric powers, our proof works only in zero characteristic.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2004, 246, 93–102

Bibliographic databases:

UDC: 512.7
Received in February 2004
Language: English

Citation: V. A. Voevodskii, “On the Zero Slice of the Sphere Spectrum”, Algebraic geometry: Methods, relations, and applications, Collected papers. Dedicated to the memory of Andrei Nikolaevich Tyurin, corresponding member of the Russian Academy of Sciences, Tr. Mat. Inst. Steklova, 246, Nauka, Moscow, 2004, 106–115; Proc. Steklov Inst. Math., 246 (2004), 93–102

Citation in format AMSBIB
\by V.~A.~Voevodskii
\paper On the Zero Slice of the Sphere Spectrum
\inbook Algebraic geometry: Methods, relations, and applications
\bookinfo Collected papers. Dedicated to the memory of Andrei Nikolaevich Tyurin, corresponding member of the Russian Academy of Sciences
\serial Tr. Mat. Inst. Steklova
\yr 2004
\vol 246
\pages 106--115
\publ Nauka
\publaddr Moscow
\jour Proc. Steklov Inst. Math.
\yr 2004
\vol 246
\pages 93--102

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    This publication is cited in the following articles:
    1. Levine M., “The homotopy coniveau tower”, Journal of Topology, 1:1 (2008), 217–267  crossref  mathscinet  zmath  isi
    2. Levine M., “Motivic Homotopy Theory”, Milan Journal of Mathematics, 76:1 (2008), 165–199  crossref  mathscinet  zmath  isi
    3. Gepner D., Snaith V., “On the Motivic Spectra Representing Algebraic Cobordism and Algebraic K–Theory”, Documenta Mathematica, 14 (2009), 359–396  mathscinet  zmath  isi
    4. Pelaez P., “Mixed motives and the slice filtration”, Comptes Rendus Mathematique, 347:9–10 (2009), 541–544  crossref  mathscinet  zmath  isi
    5. Voevodsky V., “Motives over simplicial schemes”, Journal of K–Theory, 5:1 (2010), 1–38  crossref  mathscinet  zmath  isi
    6. Spitzweck M., “Relations Between Slices and Quotients of the Algebraic Cobordism Spectrum”, Homology Homotopy Appl, 12:2 (2010), 335–351  crossref  mathscinet  zmath  isi
    7. Voevodsky V., “Motivic Eilenberg-Maclane Spaces”, Publications Mathematiques de l IHES, 2010, no. 112, 1–99  crossref  mathscinet  zmath  isi
    8. Hu P., Kriz I., Ormsby K., “Remarks on motivic homotopy theory over algebraically closed fields”, J K Theory, 7:1 (2011), 55–89  crossref  mathscinet  zmath  isi
    9. Pelaez P., “On the Orientability of the Slice Filtration”, Homology Homotopy Appl, 13:2 (2011), 293–300  crossref  mathscinet  zmath  isi
    10. Spitzweck M., “Slices of motivic Landweber spectra”, J K Theory, 9:1 (2012), 103–117  crossref  mathscinet  zmath  isi
    11. Spitzweck M., Ostvaer P.A., “Motivic Twisted K-Theory”, Algebr. Geom. Topol., 12:1 (2012), 565–599  crossref  mathscinet  zmath  isi
    12. Levine M., “a Comparison of Motivic and Classical Stable Homotopy Theories”, J. Topol., 7:2 (2014), 327–362  crossref  mathscinet  zmath  isi
    13. Dai Sh., Levine M., “Connective Algebraic K-Theory”, J. K-Theory, 13:1 (2014), 9–56  crossref  mathscinet  zmath  isi  elib
    14. Levine M., “An Overview of Motivic Homotopy Theory”, Acta Math. Vietnam, 41:3 (2016), 379–407  crossref  mathscinet  zmath  isi  elib  scopus
    15. Hill M.A., Hopkins M.J., Ravenel D.C., “On the nonexistence of elements of Kervaire invariant one”, Ann. Math., 184:1 (2016), 1–262  crossref  mathscinet  zmath  isi  scopus
    16. Rondigs O., Ostvaer P.A., “Slices of hermitian K?theory and Milnor?s conjecture on quadratic forms”, Geom. Topol., 20:2 (2016), 1157–1212  crossref  mathscinet  zmath  isi  elib  scopus
    17. Roendigs O., Ostvaer P.A., “The multiplicative structure on the graded slices of hermitian $K$-theory and Witt-theory”, Homol. Homotopy Appl., 18:1 (2016), 373–380  crossref  mathscinet  zmath  isi
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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