Balancedness of complete cohomology with respect to subcategories

Shoutao Guo; Li Liang; Xiaoyan Yang

doi:10.5802/crmath.755

Article de recherche - Algèbre

Balancedness of complete cohomology with respect to subcategories
[Propriété d’équilibre de la cohomologie complète par rapport aux sous-catégories]

Shoutao Guo ¹ ; Li Liang ^1,² ; Xiaoyan Yang ³

¹ Department of Mathematics, Gansu Center for Fundamental Research in Complex Systems Analysis and Control, Lanzhou Jiaotong University, Lanzhou 730070, China
² Gansu Provincial Research Center for Basic Disciplines of Mathematics and Statistics, Lanzhou 730070, China
³ School of Science, Zhejiang University of Science and Technology, Hangzhou, 310012, China

Comptes Rendus. Mathématique, Volume 363 (2025), pp. 705-722.

Abstract (VO)
Résumé

We study the balancedness of complete cohomology with respect to a special preenveloping/precovering subcategory. As an application, a balanced result for Tate cohomology is given.

Dans cet article, nous étudions la propriété d’équilibre de la cohomologie complète par rapport à une sous-catégorie spéciale pré-enveloppante/pré-couvrante. Comme application, nous démontrons une propriété d’équilibre pour la cohomologie de Tate.

Reçu le : 2023-10-21
Révisé le : 2025-04-30
Accepté le : 2025-04-30
Publié le : 2025-06-23

DOI : 10.5802/crmath.755

Classification : 18G25, 16E30, 16E05
Keywords: Satellite, balancedness, complete cohomology, Tate cohomology
Mots-clés : Satellite, équilibre, cohomologie complète, cohomologie de Tate

Affiliations des auteurs :

Shoutao Guo ¹ ; Li Liang ^{1, 2} ; Xiaoyan Yang ³

¹ Department of Mathematics, Gansu Center for Fundamental Research in Complex Systems Analysis and Control, Lanzhou Jiaotong University, Lanzhou 730070, China
² Gansu Provincial Research Center for Basic Disciplines of Mathematics and Statistics, Lanzhou 730070, China
³ School of Science, Zhejiang University of Science and Technology, Hangzhou, 310012, China

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Shoutao Guo and Li Liang and Xiaoyan Yang},
     title = {Balancedness of complete cohomology with respect to subcategories},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {705--722},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {363},
     year = {2025},
     doi = {10.5802/crmath.755},
     language = {en},
}

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Shoutao Guo; Li Liang; Xiaoyan Yang. Balancedness of complete cohomology with respect to subcategories. Comptes Rendus. Mathématique, Volume 363 (2025), pp. 705-722. doi : 10.5802/crmath.755. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.755/

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