Resolute stratifications for affine-space bundles

Determine whether a smooth fibrewise affine-space bundle can be trivialized after stratifying its base by resolute schemes, thereby establishing the affine-bundle relation in the Grothendieck ring of resolute varieties.

Background

For a smooth fibrewise affine-space bundle, the paper proves the corresponding relation in the Grothendieck ring of resolvable motives using motivic homotopy theory. The analogous relation in the Grothendieck ring of resolute varieties would ordinarily be proved by stratifying the base into pieces over which the bundle is trivial.

The authors explain that they have limited control over whether such a stratification can be chosen with all strata resolute. Thus, the validity of the affine-bundle relation directly in the Grothendieck ring of resolute varieties remains unresolved.

References

However, as one has very limited control over how such strata are chosen, it is unclear if one may trivialize using a stratification by resolute schemes.

— Grothendieck ring of varieties and at-the-characteristic numerical invariants  (2610.02690 - Annala et al., 2 Oct 2026) in Remark following Example 2.15, Section 2.2