Seminar in Real & Complex Geometry

Thursday, 28.02.2013, 16:30-17:30, Schreiber building, room 210

Liran Shaul, Weizmann Institute

Rigid dualizing complexes over commutative adic rings


We study rigid dualizing complexes in the category of adic rings. First, we recall the notions of derived categories, dualizing complexes, the Greenlees-May duality and rigid dualizing complexes. To develop the theory of rigid dualizing complexes over adic rings, we first extend the Greenlees-May duality to the category of DG-algebras. Next, we study Kahler differentials over adic rings. We establish the local structure of smooth maps in the category of adic rings. We use certain DG-algebra resolutions, called addically free resolutions, to study the derived relative torsion functor. Finally, we use the above theory to establish existence, uniqueness and functoriality of rigid dualizing complexes over a base ring which is regular and noetherian. Based on P.hd thesis written under supevision of Prof. Amnon Yekutieli.