Existence of the motivic t-structure on Voevodsky’s motivic category

Establish a motivic t-structure on Voevodsky’s stable infinity-category D_mot(S) of motivic sheaves for an arbitrary scheme S, i.e., construct a t-structure on D_mot(S) that would serve as the motivic t-structure in this context.

Background

Voevodsky’s framework provides a stable infinity-category D_mot(S) of motivic sheaves over a scheme S equipped with the six functors formalism. Despite this powerful structure, a central structural feature—the motivic t-structure—has not been constructed in general.

The authors mention this long-standing gap in the Introduction as part of the broader context motivating their approach to Berkovich motives, emphasizing that while many formal properties are accessible, the motivic t-structure on D_mot(S) remains an open issue.