Morel's conjecture on the motivic homotopy sheaves of punctured affine space
Morel's conjecture on the motivic homotopy sheaves of punctured affine space
Let be an integer. Write for the unramified Milnor K-theory sheaf, for the th -homotopy sheaf of punctured affine -space, and for the Nisnevich sheaf associated to the presheaf of higher Hermitian K-theory. An exact sequence of unramified Nisnevich sheaves is conjectured:
Morel's conjecture.
This conjecture describes the motivic homotopy sheaf of punctured affine space through Milnor K-theory and higher Hermitian K-theory. It has recently been settled in characteristic zero by Asok, Bachmann, and Hopkins.
Sources & referencesView supporting material
Primary source
Frédéric Déglise, “Motivic homotopy theory and stable homotopy groups”, arXiv:2510.17778 (2025).
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