The first stable homotopy groups of motivic spheres

Pages 1-74 from Volume 189 (2019), Issue 1 by Oliver Röndigs, Markus Spitzweck, Paul Arne Ostvær

Abstract

We compute the $1$-line of stable homotopy groups of motivic spheres over fields of characteristic not two in terms of hermitian and Milnor $K$-groups. This is achieved by solving questions about convergence and differentials in the slice spectral sequence.

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      author = {Hu, P. and Kriz, I. and Ormsby, K.},
      title = {Convergence of the motivic {A}dams spectral sequence},
      journal = {J. $K$-{T}heory},
      fjournal = {Journal of $K$-Theory. $K$-Theory and its {A}pplications in {A}lgebra, {G}eometry, {A}nalysis \& {T}opology},
      volume = {7},
      year = {2011},
      number = {3},
      pages = {573--596},
      issn = {1865-2433},
      mrclass = {14F42 (55T15)},
      mrnumber = {2811716},
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      doi = {10.1017/is011003012jkt150},
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      title = {The indecomposable {$K_3$} of fields},
      journal = {Ann. Sci. École Norm. Sup. (4)},
      fjournal = {Annales Scientifiques de l'École Normale Supérieure. Quatrième Série},
      volume = {22},
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      issn = {0012-9593},
      mrclass = {11R70 (12G05 18F25 19D55 19F27)},
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      url = {http://www.numdam.org/item?id=ASENS_1989_4_22_2_255_0},
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      mrclass = {14C25 (14F42 19E08 19E15 55P42)},
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      doi = {10.1112/jtopol/jtm004},
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      mrclass = {14C25 (14F42 19E08 19E15 55P42)},
      mrnumber = {3217623},
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      doi = {10.1112/jtopol/jtt031},
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      author = {Röndigs, Oliver and {\O}stv{æ}r, Paul Arne},
      title = {Motives and modules over motivic cohomology},
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Keywords
, ,
Mathematical Subject Classification
Primary: ,
DOI
https://doi.org/10.4007/annals.2019.189.1.1
MR
3898173
zbMATH
07003144
Milestones
Received: 3 September 2016
Revised: 1 February 2018
Accepted: 6 August 2018
Published online: 11 January 2019

Authors

Oliver Röndigs

Institut für Mathematik, Universität Osnabrück, Germany

Markus Spitzweck

Institut für Mathematik, Universität Osnabrück, Germany

Paul Arne Ostvær

Department of Mathematics, University of Oslo, Norway