Proves L_n to S_b^{-1}Sm(F) is fully faithful exactly for n=0, with infinite fibers in L_n to L_N transitions for n>=1 and a dimension threshold making X x A^r -> X invertible in L_n only if dim X + r <= n-1 when <=n.
arXiv preprint arXiv:2311.00092 , year=
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Birational localization of motivic spaces over perfect fields is equivalent to S^{2,1}-nullification, making π0^{b A^1} a birational invariant for proper schemes.
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Dimension filtrations in birational localisation
Proves L_n to S_b^{-1}Sm(F) is fully faithful exactly for n=0, with infinite fibers in L_n to L_N transitions for n>=1 and a dimension threshold making X x A^r -> X invertible in L_n only if dim X + r <= n-1 when <=n.
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Birational Algebraic Topology
Birational localization of motivic spaces over perfect fields is equivalent to S^{2,1}-nullification, making π0^{b A^1} a birational invariant for proper schemes.