Adic Finiteness: Bounding Homology and Applications

2016/02/10 by Sean Sather-Wagstaff, Sather-Wagstaff, Sean, Richard Wicklein +1 · 3 citations
Mathematics · #13C12 #13D05 #13D07 #13D09 #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #msc:13C12 #msc:13D05 #msc:13D07 #msc:13D09

paper · pdf · doi:10.48550/arxiv.1602.03225

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

arxiv created 2016/02/23 · arxiv updated 2016/02/25

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 R of prime characteristic is regular if and only if for some proper ideal \mathfrak b the derived local cohomology complex RΓ_\mathfrakb(R) has finite flat dimension when viewed through some positive power of the Frobenius endomorphism.

Citations

• Support and adic finiteness for complexes
• Adic semidualizing complexes
• Adically Finite Chain Complexes
• Extended Local Cohomology and Local Homology
• Adic Foxby Classes

Cited by

• Adic semidualizing complexes
• Adically Finite Chain Complexes
• Extended Local Cohomology and Local Homology
• Adic Foxby Classes

Related

• Depth and amplitude for unbounded complexes
• Local cohomology bounds and test ideals
• Regularity and finite injective dimension in characteristic p>0
• The Frobenius endomorphism and homological dimensions
• Support and adic finiteness for complexes