SMOOTH AFFINE MODEL FOR THE FRAMED CORRESPONDENCES SPECTRUM

摘要

Morel-Voevodsky's unstable pointed motivic homotopy category H_●(k) over an infinite perfect field is considered. For a smooth affine scheme Y over k, a smooth ind-scheme F_l (Y) and an open sub-scheme E_l(Y) are constructed for all I > 0, so that the motivic space F_l(Y)/E_l(Y) is equivalentin H_●(k) to the motivic space Ω_(P~1)~∞∑_(p~1)~∞(Y × T~l), T = (A~1/A~1 - 0), l > 0. The construction is notfunctorial on the category of affine schemes but is functorial on the category of so-called framed schemes constructed for this purpose.