The twisted inverse image pseudofunctor over commutative DG rings and perfect base change

Liran Shaul

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

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 H0(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 languageEnglish
Pages (from-to)279-328
Number of pages50
JournalAdvances in Mathematics
Volume320
DOIs
StatePublished - 7 Nov 2017
Externally publishedYes

Keywords

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

ASJC Scopus subject areas

  • General Mathematics

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