Base Change Along the Frobenius Endomorphism and the Gorenstein Property

2019/10/27 by Pinches Dirnfeld, Dirnfeld, Pinches
Mathematics · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1910.12315

openalex publication_date 2019/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let R be a local ring of positive characteristic and X a complex with nonzero finitely generated homology and finite injective dimension. We prove that if derived base change of X via the Frobenius (or more generally, via a contracting) endomorphism has finite injective dimension then R is Gorenstein.

Related

• G-dimension over local homomorphisms. Applications to the Frobenius endomorphism
• Gorenstein Dimensions under Base Change
• Using semidualizing complexes to detect Gorenstein rings
• The Frobenius endomorphism and homological dimensions
• Gorenstein dimensions of unbounded complexes and faithfully flat change of base (With an appendix by Driss Bennis)