English

Adic Finiteness: Bounding Homology and Applications

Commutative Algebra 2016-02-25 v2

Abstract

We prove a versions of amplitude inequalities of Iversen, Foxby and Iyengar, and Frankild and Sather-Wagstaff that replace finite generation conditions with adic finiteness conditions. As an application, we prove that a local ring RR of prime characteristic is regular if and only if for some proper ideal b\mathfrak b the derived local cohomology complex RΓb(R)\mathbf{R}\Gamma_{\mathfrak{b}}(R) has finite flat dimension when viewed through some positive power of the Frobenius endomorphism.

Keywords

Cite

@article{arxiv.1602.03225,
  title  = {Adic Finiteness: Bounding Homology and Applications},
  author = {Sean Sather-Wagstaff and Richard Wicklein},
  journal= {arXiv preprint arXiv:1602.03225},
  year   = {2016}
}

Comments

25 pages. part 3 of a series with arXiv:1401.6925, arXiv:1506.07052, arXiv:1602.03224, arXiv:1602.03226, and arXiv:1602.03227. comments welcome. v.2 has updated references and updated URL for Sather-Wagstaff

R2 v1 2026-06-22T12:47:14.116Z