Seminar in Real & Complex Geometry
Thursday, 28.02.2013, 16:30-17:30,
building, room 210
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.