A1-Algebraic Topology over a Field

By F. Morel. 2012

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Hermitian K-theory, derived equivalences and Karoubi's fundamental theorem (2012, background): “These groups naturally occur in A(1)-homotopy theory [Mor12], [AF14] and are to oriented Chow groups what algebraic K-theory is to ordinary Chow groups.”
La réalisation étale et les opérations de Grothendieck (2014, background): “Morel [32, 35] permet de vérifier la condition (SSp) sans hypothèse sur Λ ; ceci est expliqué dans l’Annexe C.”
Fundamental classes in motivic homotopy theory (2018, background): “Another motivation is Morel’s work [Mor12] on computations of homotopy groups, in which a crucial role is played by the construction of good transfer maps for finite field extensions in the unstable homotopy category.”
Aspects of Enumerative Geometry with Quadratic Forms (2017, methodology): “Here KMW n (L) is the nth Milnor-Witt sheaf, as defined by Hopkins-Morel [34, 35], twisted by a line bundle L onX.”
A quadratic refinement of the Grothendieck-Lefschetz-Verdier trace formula (2013, background): “1k/: 1This result is proved by Morel in [20] under the assumption that k is perfect.”