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Title
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The twisted inverse image pseudofunctor over commutative DG rings and perfect base change
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Author
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Abstract
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| Let K be a Gorenstein noetherian ring of finite Krull dimension, and consider the category of cohomologically noetherian commutative differential graded rings A over K, such that H-0 (A) is essentially of finite type over K, and A has finite flat dimension over K. We extend Grothendieck's twisted inverse image pseudofunctor to this category by generalizing the theory of rigid dualizing complexes to this setup. We prove functoriality results with respect to cohomologically finite and cohomologically essentially smooth maps, and prove a perfect base change result for f(!) in this setting. As application, we deduce a perfect derived base change result for the twisted inverse image of a map between ordinary commutative noetherian rings. Our results generalize and solve some recent conjectures of Yekutieli. (C) 2017 Elsevier Inc. All rights reserved. |
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Language
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English
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Source (journal)
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Advances in mathematics. - New York, N.Y.
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Publication
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New York, N.Y.
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2017
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ISSN
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0001-8708
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DOI
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10.1016/J.AIM.2017.08.041
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Volume/pages
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320
(2017)
, p. 279-328
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ISI
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000413884400008
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Full text (Publisher's DOI)
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Full text (publisher's version - intranet only)
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