Reconstructing rational stable motivic homotopy theory

Using a recent computation of the rational minus part of $SH(k)$ by Ananyevskiy, Levine and Panin, a theorem of Cisinski and Déglise and a version of the Röndigs and Østvær theorem, rational stable motivic homotopy theory over an infinite perfect field of characteristic different from 2 is recovered in this paper from finite Milnor–Witt correspondences in the sense of Calmès and Fasel.

[1]  I. Panin,et al.  Framed motives of algebraic varieties (after V. Voevodsky) , 2014, Journal of the American Mathematical Society.

[2]  Haakon Kolderup.  Homotopy Invariance of Nisnevich Sheaves with Milnor-Witt Transfers , 2017, Documenta Mathematica.

[3]  Joël Riou,et al.  Algebraic elliptic cohomology theory and flops I , 2013, Mathematische Annalen.

[4]  Denis-Charles Cisinski,et al.  Triangulated Categories of Mixed Motives , 2009, Springer Monographs in Mathematics.

[5]  G. Garkusha.  Comparing motives of smooth algebraic varieties , 2017, Comptes Rendus Mathematique.

[6]  Tom Bachmann.  Motivic and real étale stable homotopy theory , 2016, Compositio Mathematica.

[7]  J. Fasel,et al.  A cancellation theorem for Milnor-Witt correspondences , 2017, 1708.06098.

[8]  F. D'eglise,et al.  MW-motivic complexes , 2017, 1708.06095.

[9]  E. Elmanto,et al.  Modules over Milnor-Witt Motivic Cohomology , 2017 .

[10]  I. Panin,et al.  Framed motives of relative motivic spheres , 2016, 1604.02732.

[11]  Hassan J. Al Hwaeer,et al.  Grothendieck categories of enriched functors. , 2016 .

[12]  I. Panin,et al.  Cancellation theorem for framed motives of algebraic varieties , 2016, 1601.06642.

[13]  I. Panin,et al.  Witt sheaves and the η ‐inverted sphere spectrum , 2015, 1504.04860.

[14]  V. Voevodsky.  Triangulated categories of motives over a field , 2015 .

[15]  B. Calmès,et al.  Finite Chow-Witt correspondences , 2014, 1412.2989.

[16]  I. Panin,et al.  The triangulated category of K-motives DK , 2014 .

[17]  P. Ostvaer,et al.  The motivic Steenrod algebra in positive characteristic , 2013, 1305.5690.

[18]  I. Panin,et al.  The triangulated category of K-motives DK_(k) , 2013, 1302.2163.

[19]  V. Voevodsky.  3. Cohomological Theory of Presheaves with Transfers , 2011 .

[20]  I. Panin,et al.  K-motives of algebraic varieties , 2011, 1108.0375.

[21]  P. A. Østvær,et al.  Modules over motivic cohomology , 2008 .

[22]  P. A. Østvær,et al.  Rigidity in motivic homotopy theory , 2008 .

[23]  Jeanne Fasel.  Groupes de Chow-Witt , 2008 .

[24]  Denis-Charles Cisinski,et al.  Local and stable homological algebra in Grothendieck abelian categories , 2007, 0712.3296.

[25]  萩原啓（東京大学）.  An introduction to A^1-homotopy theory (1)-(2) , 2007 .

[26]  F. Morel.  The Stable [graphic]$$\mathbb{A}^1$$-Connectivity Theorems , 2006 .

[27]  Daniel R. Grayson.  The Motivic Spectral Sequence* , 2004 .

[28]  F. Morel.  On the Motivic π0 of the Sphere Spectrum , 2004 .

[29]  B. Dundas,et al.  Motivic functors , 2003, Documenta Mathematica.

[30]  A. Suslin.  On the Grayson Spectral Sequence , 2003 .

[31]  Mark Hovey.  Spectra and symmetric spectra in general model categories , 2000, math/0004051.

[32]  J. Jardine.  Motivic symmetric spectra , 2000, Documenta Mathematica.

[33]  Vladimir Voevodsky,et al.  Cycles, Transfers And Motivic Homology Theories , 2000 .

[34]  A. Suslin,et al.  Bloch-Kato Conjecture and Motivic Cohomology with Finite Coefficients , 2000 .

[35]  Vladimir Voevodsky,et al.  A1-homotopy theory of schemes , 1999 .

[36]  B. Shipley,et al.  Algebras and Modules in Monoidal Model Categories , 1998, math/9801082.

[37]  Amnon Neeman,et al.  The Grothendieck duality theorem via Bousfield’s techniques and Brown representability , 1996 .

[38]  Alan Robinson.  The extraordinary derived category , 1987 .

[39]  B. Day.  On closed categories of functors , 1970 .

[40]  Jean-Pierre Serre,et al.  Groupes d'homotopie et classes des groupes abeliens , 1953 .

[41]  V. Voevodsky.  Cohomological theory of presheaves with transfers , 2022 .