Telescope conjecture, idempotent ideals, and the transfinite radical

We show that for an artin algebra $Λ$, the telescope conjecture for module categories is equivalent to certain idempotent ideals of mod-$Λ$ being generated by identity morphisms. As a consequence, we prove the conjecture for domestic standard selfinjective algebras and domestic special biserial algebras. We achieve this by showing that in any Krull-Schmidt category with local d.c.c. on ideals, any idempotent ideal is generated by identity maps and maps from the transfinite radical.

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