Yen Ngoc Do, Tri Minh Nguyen, Nam Tuan Tran Posts and Telecommunications Institute of Technology; Ton Duc Thang University; Ho Chi Minh University of Pedagogy
Abstract : We prove some results about the finiteness of co-associated primes of generalized local homology modules inspired by a conjecture of Grothendieck and a question of Huneke. We also show some equivalent properties of minimax local homology modules. By duality, we get some properties of Herzog's generalized local cohomology modules.
Keywords : Linearly compact module, (generalized) local homology, (generalized) local cohomology, (co-)associated prime
MSC numbers : 13D45
Supported by : This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant No. 101.04-2018.304
The nal work of this paper was done when the authors visited Vietnam Institute for Advanced Study in Mathematics (VIASM). We would like to thank VIASM for hospitality and financial support. We also thank the Domestic PhD Scholarship Programme of Vingroup Innovation Foundation.