Title of Seminar: Algebraic Geometry Preprint Seminar 2025
Title of Talk: Morita theory for the derived category of schemes
Speaker: Charanya Ravi
Date: February 17, 2025
Time: 16:00:00 Hours
Venue: AG-77
Abstract: A theorem of Rickard from 1989 shows that if R and S are rings, then a derived equivalence between R and S is independent of the choice of derived categories of modules over the rings. That is, if D^?(R-#) and D^?(S-#) are equivalent as triangulated categories for appropriate choices of ? = +, - or b and # = Mod, proj or mod, then they are equivalent for every other choice of decorations. In this case, the two rings are said to be derived equivalent. In this talk, following the recent work of Canonaco-Neeman-Stellari (arXiv:2402.04605), we review a vast generalization of this result to quasi-compact and quasi-separated schemes. The main idea is to use the framework of weakly approximable triangulated categories and show that all the `classical? and naturally defined full triangulated subcategories of these are intrinsic.
Title of Talk: Morita theory for the derived category of schemes
Speaker: Charanya Ravi
Date: February 17, 2025
Time: 16:00:00 Hours
Venue: AG-77
Abstract: A theorem of Rickard from 1989 shows that if R and S are rings, then a derived equivalence between R and S is independent of the choice of derived categories of modules over the rings. That is, if D^?(R-#) and D^?(S-#) are equivalent as triangulated categories for appropriate choices of ? = +, - or b and # = Mod, proj or mod, then they are equivalent for every other choice of decorations. In this case, the two rings are said to be derived equivalent. In this talk, following the recent work of Canonaco-Neeman-Stellari (arXiv:2402.04605), we review a vast generalization of this result to quasi-compact and quasi-separated schemes. The main idea is to use the framework of weakly approximable triangulated categories and show that all the `classical? and naturally defined full triangulated subcategories of these are intrinsic.