Reduction techniques for homological conjectures

DOI10.21099/tkbjm/1496162134zbMath0809.16021OpenAlexW1951788695WikidataQ123166372 ScholiaQ123166372MaRDI QIDQ1316495

Dieter Happel

Publication date: 3 April 1995

Published in: Tsukuba Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.21099/tkbjm/1496162134

zbMATH Keywords

finite dimensional algebrastilting modulestriangulated categoriesrecollementfinitistic dimension conjecturederived category of bounded complexesvanishing conjecturegeneralized Nakayama conjecture

Mathematics Subject Classification ID

Finite rings and finite-dimensional associative algebras (16P10) Representations of orders, lattices, algebras over commutative rings (16G30) Homological dimension in associative algebras (16E10)

Related Items (45)

Reducing homological conjectures by \(n\)-recollements ⋮ Finiteness of finitistic dimension is invariant under derived equivalences. ⋮ Jordan-Hölder theorems for derived categories of derived discrete algebras ⋮ On the combinatorics of the set of tilting modules ⋮ Bimodule monomorphism categories and RSS equivalences via cotilting modules ⋮ Ladders of compactly generated triangulated categories and preprojective algebras ⋮ Silting reduction and Calabi–Yau reduction of triangulated categories ⋮ Homological theory of recollements of abelian categories ⋮ Symmetric subcategories, tilting modules, and derived recollements ⋮ Relative homological dimensions in recollements of triangulated categories ⋮ Recollements and Hochschild theory. ⋮ Constructions of derived equivalences for algebras and rings ⋮ Gluing simple-minded collections in triangulated categories ⋮ Eventually homological isomorphisms in recollements of derived categories ⋮ Ring constructions and generation of the unbounded derived module category ⋮ Extension dimensions of derived and stable equivalent algebras ⋮ Gorensteinness, homological invariants and Gorenstein derived categories ⋮ Jordan-Hölder theorems for derived module categories of piecewise hereditary algebras. ⋮ Derived equivalences between matrix subrings and their applications ⋮ Tilting complexes and Auslander-Reiten conjecture. ⋮ Stratifying derived module categories ⋮ Recollement of colimit categories and its applications ⋮ On the finitistic dimension conjecture. III: Related to the pair \(eAe\subseteq A\). ⋮ Dlab's theorem and tilting modules for stratified algebras. ⋮ Syzygy properties under recollements of derived categories ⋮ Recollements and homological dimensions ⋮ Generalized Auslander-Reiten conjecture and tilting equivalences ⋮ Dominant dimensions, derived equivalences and tilting modules ⋮ Exact contexts, noncommutative tensor products, and universal localizations ⋮ Upper recollements and triangle expansions ⋮ On the uniqueness of stratifications of derived module categories. ⋮ \(\mathcal D\)-split sequences and derived equivalences. ⋮ Cohomological stratification of diagram algebras. ⋮ Ladders of recollements of abelian categories ⋮ Recollements of derived categories. I: Construction from exact contexts ⋮ Adjoint functors and representation dimensions ⋮ On the recollements of functor categories ⋮ Gorenstein algebras and recollements ⋮ Reduction techniques for the finitistic dimension ⋮ Good tilting modules and recollements of derived module categories. II ⋮ A representation-theoretic approach to recollements of abelian categories ⋮ Strong global dimensions of triangulated categories with respect to silting objects ⋮ Unbounded derived categories and the finitistic dimension conjecture ⋮ Lifting of recollements and gluing of partial silting sets ⋮ Recollements and stratifying ideals

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