On the Motivic π0 of the Sphere Spectrum

By F. Morel. 2004

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Mixed Weil cohomologies (2007, background): “9 In [43], DA1 (S,R) is defined using non-symmetric spectra instead of symmetric spectra.”
The Mayer-Vietoris principle for Grothendieck-Witt groups of schemes (2008, background): “Grothendieck-Witt groups naturally occur in A1-homotopy theory [19] and are to oriented Chow groups what algebraic K-theory is to ordinary Chow groups; see [3, 6, 11].”
Low-dimensional Milnor–Witt stems over ℝ (2015, methodology): “[Morel 2004b] F. Morel, “On the motivic π0 of the sphere spectrum”, pp. 219–260 in Axiomatic, enriched and motivic homotopy theory, edited by J. P. C. Greenlees, NATO Sci. Ser. II Math.”
A1-Algebraic Topology over a Field (2012, methodology): “Our computations thus clearly stabilize as follows: Corollary 21 [31, 30] Let SH(k) be the stable A1-homotopy category of P1spectra (or T -spectra) over k [50, 31, 30].”
The norm residue isomorphism theorem (2009, methodology): “We will describe this functor in Section 2; other references are [11, 15, 32, 34].”
The class of Eisenbud–Khimshiashvili–Levine is the local A1-Brouwer degree (2016, background): “For endomorphisms of P(1)k, these notions and properties are stated in [Mor04] [Mor06], and build on ideas of J.”