Michal Hrbek, The Czech Academy of Sciences, Prague
Title: Telescope conjecture for t-structures in
derived categories
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. Indeed, 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.