Adically Finite Chain Complexes

2016/02/10 by Sean Sather-Wagstaff, Sather-Wagstaff, Sean, Richard Wicklein +1 · 3 citations
Mathematics · #13B35 #13C12 #13D07 #13D09 #13D45 #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #msc:13B35 #msc:13C12 #msc:13D07 #msc:13D09 #msc:13D45

paper · pdf · doi:10.48550/arxiv.1602.03224

20 pages. part 2 of a series with arXiv:1401.6925, arXiv:1506.07052, arXiv:1602.03225, arXiv:1602.03226, and arXiv:1602.03227. comments welcome. v.2 has updated references and URL for Sather-Wagstaff

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

Abstract

We investigate the similarities between adic finiteness and homological finiteness for chain complexes over a commutative noetherian ring. In particular, we extend the isomorphism properties of certain natural morphisms from homologically finite complexes to adically finite complexes. We do the same for characterizations of certain homological dimensions. In addition, we study transfer of adic finiteness along ring homomorphisms, all with a view toward subsequent applications.

Citations

• Support and adic finiteness for complexes
• Adic semidualizing complexes
• Adic Finiteness: Bounding Homology and Applications
• Extended Local Cohomology and Local Homology
• Adic Foxby Classes

Cited by

• Adic Finiteness: Bounding Homology and Applications
• Extended Local Cohomology and Local Homology
• Adic Foxby Classes

Related

• Support and adic finiteness for complexes
• Adic Finiteness: Bounding Homology and Applications
• Contracting endomorphisms and dualizing complexes
• Shellability and Regularity of Chain Complexes over a Principal Ring
• Properties of cellular classes of chain complexes