Over characteristic 0 fields, the unit map from the motivic sphere spectrum to the special linear cobordism spectrum MSL is an isomorphism on homotopy modules, proven by comparing framed and SL-oriented framed correspondences.
A comparison theorem for MW-motivic cohomology
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abstract
We prove that for a finitely generated field over an infinite perfect field k, and for any integer n, the (n,n)-th MW-motivic cohomology group identifies with the n-th Milnor-Witt K-theory group of that field
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The unit map of the algebraic special linear cobordism spectrum
Over characteristic 0 fields, the unit map from the motivic sphere spectrum to the special linear cobordism spectrum MSL is an isomorphism on homotopy modules, proven by comparing framed and SL-oriented framed correspondences.