## Abstract

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.

Original language | English |
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Pages (from-to) | 279-328 |

Number of pages | 50 |

Journal | Advances in Mathematics |

Volume | 320 |

DOIs | |

State | Published - 7 Nov 2017 |

Externally published | Yes |

## Keywords

- Cohomologically finite homomorphism
- Cohomologically smooth homomorphism
- Commutative DG-algebra
- Grothendieck duality
- Rigid dualizing complex

## ASJC Scopus subject areas

- General Mathematics