Motivic Bass finite-generation conjecture

Prove that for every regular scheme Y of finite type over the integers, the motivic cohomology groups H^a(Y,Z(b)) are finitely generated for all integers a and b.

Background

The motivic Bass conjecture is invoked to derive finite generation of higher Chow groups over global fields. Combined with the paper’s unique-divisibility results, finite generation implies vanishing in the range 2i-j≥3 for the relevant smooth proper varieties.

The conjecture is formulated for all motivic cohomology degrees and weights of regular schemes of finite type over Z.

References

Let $Y$ be a regular scheme of finite type over $Z$. Then $Ha(Y,Z(b))$ is finitely generated for all integers $a$ and $b$.

— Divisibility and torsion in higher Chow groups over arithmetic fields  (2609.11178 - Hiranouchi et al., 10 Sep 2026) in Conjecture 5.1, Section 5, subsection “Global fields”