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.
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