TY - JOUR

T1 - Smooth Affine Model for the Framed Correspondences Spectrum

AU - Druzhinin, A.

N1 - Publisher Copyright: © 2021, Springer Science+Business Media, LLC, part of Springer Nature.

PY - 2021/2

Y1 - 2021/2

N2 - 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 Fl(Y) and an open subscheme El(Y) are constructed for all l > 0, so that the motivic space Fl(Y)/El(Y) is equivalent in H●(k) to the motivic space Ωℙ1∞∑ℙ1∞(Y×Tl),T=(A1/A1−0),l>0. The construction is not functorial on the category of affine schemes but is functorial on the category of so-called framed schemes constructed for this purpose.

AB - 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 Fl(Y) and an open subscheme El(Y) are constructed for all l > 0, so that the motivic space Fl(Y)/El(Y) is equivalent in H●(k) to the motivic space Ωℙ1∞∑ℙ1∞(Y×Tl),T=(A1/A1−0),l>0. The construction is not functorial on the category of affine schemes but is functorial on the category of so-called framed schemes constructed for this purpose.

UR - http://www.scopus.com/inward/record.url?scp=85099472361&partnerID=8YFLogxK

U2 - 10.1007/s10958-021-05199-4

DO - 10.1007/s10958-021-05199-4

M3 - Article

AN - SCOPUS:85099472361

VL - 252

SP - 784

EP - 793

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 6

ER -