Topology and Related Topics Seminar
Thursday, 12 October 2023, 2:30 pm
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Venue: 215
Host: Rekha Santhanam
Speaker: Omkar Javadekar
Affiliation: IIT Bombay
Title: A review of derived category and related topics
Abstract: In this talk, we will see the construction of localization of a category with respect to an arbitrary class of morphisms, and define the derived category using localization. We will sketch the proof of the fact that the homotopy and derived categories are triangulated. Along the way, we will also try to revise the example of projective model structure on the category Ch(R) of chain complexes of modules over a ring R. We will then define the notion of support for objects of the derived category D(R), and end by stating the theorem of Hopkins-Neeman for small R-complexes.