Is there a non-trivial t-structure on the stable homotopy category? (one which is not given by homotopy groups) My guess is there isn't but google didn't lead me anywhere.

Same question for MU-modules

@SaalHardali i don't know, but: for t-structures on the stable homotopy category, i'd look in hovey-palmieri-strickland. in both settings, i'd expect there to exist perversions of the usual t-structure, since arithmetic localization preserves the usual notion of connectivity. i'd also expect there not to exist chromatic perversions, since the co/localizing subcategories of the chromatically localized categories are understood (in the hovey-strickland memoir) to be scarce

@EricPeterson I'll check it out, thanks!