Tuesday, November 20, 14 :00, 7.527

Michal Hrbek (Czech Academy of Sciences, Prague)
A variant of telescope conjecture for t-structures

Abstract:
Given a compactly generated triangulated category, the Telescope Conjecture (TC) asks whether any smashing localization arises from a set of compact objects. This question was originally asked by Ravenel in the setting of the stable homotopy category of spectra, and there it remains open to this day. In the algebraic setting however, namely in the case of the unbounded derived category of a ring, a lot of results have been obtained. Namely, there are examples of rings for which TC fails (first counterexample is due to Keller), but for nice enough rings, such as hereditary or commutative noetherian rings, the TC was shown to hold (Neeman, Krause-Stovicek). In this talk, we discuss a "semistable" variant of TC, in which t-structures play the role instead of localizing subcategories. Apart from the classical TC, this property generalizes another well-studied property of a derived category - the cofinite type of all cosilting complexes. The talk will include results from the recent joint works with L. Angeleri Hügel and with S. Bazzoni.