Gillespie’s questions and Grothendieck duality

Wang, Junpeng; Liu, Zhongkui; Yang, Gang

doi:10.5802/crmath.198

Algèbre

Gillespie’s questions and Grothendieck duality

Wang, Junpeng ¹ ; Liu, Zhongkui ¹ ; Yang, Gang ²

¹ Department of Mathematics, Northwest Normal University, Lanzhou 730070, People’s Republic of China
² Department of Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, People’s Republic of China

Comptes Rendus. Mathématique, Tome 359 (2021) no. 5, pp. 593-607.

Résumé

Gillespie posed two questions in [Front. Math. China 12 (2017) 97-115], one of which states that “for what rings $R$ do we have $K (AC) = K (R - Inj)$ ?”. We give an answer to such a question. As applications, we obtain a new homological approach that unifies some well-known conditions of rings such that Krause’s recollement holds, and give an example to show that there exists a Gorenstein injective module which is not Gorenstein AC-injective. We also improve Neeman’s angle of view to the Grothendieck duality for derived categories of modules from the case of left Noether and right coherent rings such that all flat left modules have finite projective dimension to the case of left and right coherent rings.

Reçu le : 2020-11-08
Révisé le : 2021-03-19
Accepté le : 2021-03-19
Publié le : 2021-07-13

DOI : 10.5802/crmath.198

Classification : 18G35, 18G05, 18G20

Affiliations des auteurs :

Wang, Junpeng ¹ ; Liu, Zhongkui ¹ ; Yang, Gang ²

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     title = {Gillespie{\textquoteright}s questions and {Grothendieck} duality},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {593--607},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {359},
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     year = {2021},
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     language = {en},
     url = {http://www.numdam.org/articles/10.5802/crmath.198/}
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Wang, Junpeng; Liu, Zhongkui; Yang, Gang. Gillespie’s questions and Grothendieck duality. Comptes Rendus. Mathématique, Tome 359 (2021) no. 5, pp. 593-607. doi : 10.5802/crmath.198. http://www.numdam.org/articles/10.5802/crmath.198/

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