Seminario MALGA Padova Verona - Moduli Algebre Anelli: “Telescope conjecture for t-structures in derived categories”

Mercoledì 12 Dicembre 2018, ore 15:00 - Sala Riunioni 701 - Michal Hrbek


Mercoledì 12 Dicembre 2018 alle ore 15:00 in Sala Riunioni 701, Michal Hrbek (The Czech Academy of Sciences, Prague) terrà un seminario dal titolo “Telescope conjecture for t-structures in derived categories” nell'ambito del Seminario Padova-Verona MALGA - Moduli Algebre Anelli.

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.