We find a condition on the underlying graph of an Artin group that fully determines if it is subgroup separable. As consequence, separable and only can be obtained from groups ranks at most 2 via finite sequence free products direct with infinite cyclic group. This result generalizes Metaftsis-Raptis criterion for Right-Angled groups.

This paper studies Artin–Tate motives over bases S ⊂ Spec OF , for a number field F . As a subcategory of motives over S, the triangulated category of Artin–TatemotivesDATM(S) is generated by motives φ∗1(n), where φ is any finite map. After establishing the stability of these subcategories under pullback and pushforward along open and closed immersions, a motivic t-structure is constructed. Exa...