Resolving dualities and applications to homological invariants
arXiv:2209.11627 · doi:10.4153/S0008414X24000580
Abstract
Dualities of resolving subcategories of finitely generated modules over Artin algebras are characterized as dualities with respect to Wakamatsu tilting bimodules. By restriction of these dualities to resolving subcategories of finitely generated modules with finite projective or Gorenstein-projective dimensions, Miyashita's duality and Huisgen-Zimmermann's correspondence on tilting modules as well as their Gorenstein version are obtained. Applications include constructing triangle equivalences of derived categories of finitely generated Gorenstein-projective modules and showing the invariance of higher algebraic -groups and semi-derived Ringel-Hall algebras of finitely generated Gorenstein-projective modules under tilting.
27 pages. Any comments or suggestions are welcome!