Geodesic
Resolving dualities and applications to homological invariants
Canadian journal of mathematics, Tome 77 (2025) no. 6, pp. 1861-1889

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DOI

Dualities of resolving subcategories of module categories over rings are introduced and characterized as dualities with respect to Wakamatsu tilting bimodules. By restriction of the dualities to smaller resolving subcategories, sufficient and necessary conditions for these bimodules to be tilting are provided. This leads to the Gorenstein version of both the Miyashita’s duality and Huisgen-Zimmermann’s correspondence. An application of resolving dualities is to show that higher algebraic K-groups and semi-derived Ringel–Hall algebras of finitely generated Gorenstein-projective modules over Artin algebras are preserved under tilting.
DOI : 10.4153/S0008414X24000580
Mots-clés : Duality, Gorenstein-projective module, resolving subcategory, semi-derived Ringel–Hall algebra, Wakamatsu tilting module 
Chen, Hongxing; Hu, Jiangsheng. Resolving dualities and applications to homological invariants. Canadian journal of mathematics, Tome 77 (2025) no. 6, pp. 1861-1889. doi: 10.4153/S0008414X24000580
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     title = {Resolving dualities and applications to homological invariants},
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     year = {2025},
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