[Stratification de catégories dérivées de modules]
On utilise la notion de recollement pour obtenir une stratification de la catégorie dérivée de la catégorie des modules sur un anneau. Ces stratifications sont des analogues des suites de composition pour les groupes et les modules. Nous sommes ainsi amenés à chercher un analogue « dérivé » du théorème de Jordan Hölder : les stratifications sont-elles uniques à lʼordre des facteurs et aux équivalences près ? Cʼest effectivement le cas pour plusieurs classes dʼanneaux, y compris les anneaux semi-simples, les anneaux commutatifs noethériens, les algèbres de groupes de groupes finis et les algèbres de dimension finie qui sont héréditaires par morceaux.
The concept of recollement is used to obtain a stratification of the derived module category of a ring which may be regarded as an analogue of a composition series for groups or modules. This analogy raises the problem whether a ‘derived’ Jordan Hölder theorem holds true; that is, are such stratifications unique up to ordering and equivalence? This is indeed the case for several classes of rings, including semi-simple rings, commutative Noetherian rings, group algebras of finite groups, and finite dimensional algebras which are piecewise hereditary.
Accepté le :
Publié le :
Lidia Angeleri Hügel 1 ; Steffen Koenig 2 ; Qunhua Liu 2 ; Dong Yang 3
@article{CRMATH_2011__349_21-22_1139_0,
author = {Lidia Angeleri H\"ugel and Steffen Koenig and Qunhua Liu and Dong Yang},
title = {Stratifying derived module categories},
journal = {Comptes Rendus. Math\'ematique},
pages = {1139--1144},
publisher = {Elsevier},
volume = {349},
number = {21-22},
year = {2011},
doi = {10.1016/j.crma.2011.06.018},
language = {en},
}
TY - JOUR AU - Lidia Angeleri Hügel AU - Steffen Koenig AU - Qunhua Liu AU - Dong Yang TI - Stratifying derived module categories JO - Comptes Rendus. Mathématique PY - 2011 SP - 1139 EP - 1144 VL - 349 IS - 21-22 PB - Elsevier DO - 10.1016/j.crma.2011.06.018 LA - en ID - CRMATH_2011__349_21-22_1139_0 ER -
Lidia Angeleri Hügel; Steffen Koenig; Qunhua Liu; Dong Yang. Stratifying derived module categories. Comptes Rendus. Mathématique, Volume 349 (2011) no. 21-22, pp. 1139-1144. doi : 10.1016/j.crma.2011.06.018. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.06.018/
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