Representation Theory of Geigle-Lenzing Complete Intersections

DOI10.1090/memo/1412zbMath1530.16001arXiv1409.0668OpenAlexW1818940219MaRDI QIDQ6045425

Osamu Iyama, Martin Herschend, Hiroyuki Minamoto, Steffen Oppermann

Publication date: 30 May 2023

Published in: Memoirs of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1409.0668

zbMATH Keywords

Cohen-Macaulay moduletilting theoryderived categoryAuslander-Reiten theoryweighted projective linecanonical algebraFano algebra\(d\)-representation infinite algebraGeigle-Lenzing projective space

Mathematics Subject Classification ID

Cohen-Macaulay modules in associative algebras (16G50) Representation type (finite, tame, wild, etc.) of associative algebras (16G60) Cohen-Macaulay modules (13C14) Homological dimension in associative algebras (16E10) Derived categories and associative algebras (16E35) Research exposition (monographs, survey articles) pertaining to associative rings and algebras (16-02)

Related Items (19)

Tilting bundles on orders on \(\mathbb P^d\) ⋮ \(n\)-abelian and \(n\)-exact categories ⋮ The category of extensions and a characterisation of \(n\)-exangulated functors ⋮ Serre functors and graded categories ⋮ Derived factorization categories of non‐Thom–Sebastiani‐type sums of potentials ⋮ Quiver combinatorics and triangulations of cyclic polytopes ⋮ Classification results for \(n\)-hereditary monomial algebras ⋮ Auslander-Gorenstein algebras from Serre-formal algebras via replication ⋮ Tensor products of \(n\)-complete algebras ⋮ Fabric idempotents and higher Auslander-Reiten theory ⋮ Large tilting sheaves over weighted noncommutative regular projective curves ⋮ 2-hereditary algebras and almost Fano weighted surfaces ⋮ Moduli stacks of Serre stable representations in tilting theory ⋮ Simplicial structures in higher Auslander-Reiten theory ⋮ \(d\)-representation-finite self-injective algebras ⋮ Higher representation infinite algebras from McKay quivers of metacyclic groups ⋮ Preprojective algebra structure on skew-group algebras ⋮ The existence of n-Auslander–Reiten sequences via determined morphisms ⋮ A RECOLLEMENT APPROACH TO GEIGLE–LENZING WEIGHTED PROJECTIVE VARIETIES

Cites Work

• Tilting bundles on orders on \(\mathbb P^d\)
• Homological mirror symmetry for Brieskorn-Pham singularities
• The representation type of Segre varieties
• Maximal modifications and Auslander-Reiten duality for non-isolated singularities
• A category of kernels for equivariant factorizations and its implications for Hodge theory
• Cluster tilting for higher Auslander algebras.
• Formal completions and idempotent completions of triangulated categories of singularities
• The structure of AS-Gorenstein algebras.
• Compact generators in categories of matrix factorizations
• Graded and filtered rings and modules
• Homology of Noetherian rings and local rings
• Tame algebras and integral quadratic forms
• Einfache Kurvensingularitäten und torsionsfreie Moduln
• Higher-dimensional Auslander-Reiten theory on maximal orthogonal subcategories.
• Auslander correspondence.
• Matrix factorizations and representations of quivers. II: Type \(ADE\) case.
• Koszul equivalences in \(A_\infty\)-algebras.
• Triangulated categories of matrix factorizations for regular systems of weights with \(\varepsilon = - 1\)
• Tilting sheaves in representation theory of algebras
• Vector bundles on complex projective spaces
• Almost split sequences in subcategories
• Localization of triangulated categories and derived categories
• Perpendicular categories with applications to representations and sheaves
• Rings mit only finitely many isomorphism classes of maximal indecomposable Cohen-Macaulay modules
• On graded rings. I
• Noncommutative projective schemes
• The classification of homogeneous Cohen-Macaulay rings of finite representation type
• Cohen-Macaulay modules on hypersurface singularities. I
• Cohen-Macaulay modules on hypersurface singularities. II
• Derived categories and stable equivalence
• Ideal classes of three-dimensional Sklyanin algebras.
• Triangle singularities, ADE-chains, and weighted projective lines
• Classifying thick subcategories of the stable category of Cohen-Macaulay modules
• Liftings and weak liftings of modules
• Tilting and cluster tilting for quotient singularities
• ACM bundles on cubic surfaces
• On tensor products of path algebras of type \(A\).
• \(n\)-representation infinite algebras.
• Mutation in triangulated categories and rigid Cohen-Macaulay modules
• Reconstruction from Koszul homology and applications to module and derived categories
• Sur les ordres commutatifs avec un nombre fini de réseaux indecomposables
• A proof of the existence of minimal R-algebra resolutions
• Residues and duality. Lecture notes of a seminar on the work of A. Grothendieck, given at Havard 1963/64. Appendix: Cohomology with supports and the construction of the \(f^!\) functor by P. Deligne
• On two examples by Iyama and Yoshino
• n -representation-finite algebras and twisted fractionally Calabi-Yau algebras
• $n$-representation-finite algebras and $n$-APR tilting
• Ampleness of two-sided tilting complexes
• Reflexive modules on quotient surface singularities.
• Noncommutative curves of genus zero: related to finite dimensional algebras
• The homological theory of maximal Cohen-Macaulay approximations
• Gromov-Witten theory of Deligne-Mumford stacks
• Fomin-Zelevinsky mutation and tilting modules over Calabi-Yau algebras
• Derived Categories of Coherent Sheaves and Triangulated Categories of Singularities
• Rational Singularities and Almost Split Sequences
• Homological Algebra on a Complete Intersection, with an Application to Group Representations
• Deriving DG categories
• Projective Dimension and the Singular Locus
• Exceptional vector bundles, tilting sheaves and tilting complexes for weighted projective lines
• Quotients of triangulated categories and Equivalences of Buchweitz, Orlov, and Amiot-Guo-Keller
• Tilting and Cluster Tilting for Preprojective Algebras and Coxeter Groups
• Weighted Projective Lines and Rational Surface Singularities
• Stable categories of Cohen-Macaulay modules and cluster categories: Dedicated to Ragnar-Olaf Buchweitz on the occasion of his sixtieth birthday
• A RECOLLEMENT APPROACH TO GEIGLE–LENZING WEIGHTED PROJECTIVE VARIETIES
• Stable module theory
• A characterization of hereditary categories with tilting object
• Tame and wild projective curves and classification of vector bundles.
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