Czechoslovak Mathematical Journal

Czechoslovak Mathematical Journal, Vol. 73, No. 2, pp. 431-452, 2023

Another version of cosupport in ${\rm D}(R)$

Junquan Qin, Xiaoyan Yang

Received August 10, 2021. Published online January 5, 2023.

Abstract: The goal of the article is to develop a theory dual to that of support in the derived category ${\rm D}(R)$. This is done by introducing `big' and `small' cosupport for complexes that are different from the cosupport in D. J. Benson, S. B. Iyengar, H. Krause (2012). We give some properties for cosupport that are similar, or rather dual, to those of support for complexes, study some relations between `big' and `small' cosupport and give some comparisons of support and cosupport. Finally, we investigate the dual notion of associated primes.

Keywords: cosupport; support; coassociated prime; associated prime

Classification MSC: 13D07, 13D09, 13E05

DOI: 10.21136/CMJ.2023.0282-21

PDF available at: Springer Institute of Mathematics CAS Digital Mathematics Library

References:
[1] D. J. Benson, S. B. Iyengar, H. Krause: Local cohomology and support for triangulated categories. Ann. Sci. Éc. Norm. Supér. (4) 41 (2008), 575-621. DOI 10.24033/asens.2076 | MR 2489634 | Zbl 1171.18007
[2] D. J. Benson, S. B. Iyengar, H. Krause: Colocalizing subcategories and cosupport. J. Reine Angew. Math. 673 (2012), 161-207. DOI 10.1515/CRELLE.2011.180 | MR 2999131 | Zbl 1271.18012
[3] M. P. Brodmann, R. Y. Sharp: Local Cohomology: An Algebraic Introduction with Geometric Applications. Cambridge Studies in Advanced Mathematics 60. Cambridge University Press, Cambridge (1998). DOI 10.1017/CBO9780511629204 | MR 1613627 | Zbl 0903.13006
[4] L. W. Christensen: Sequences for complexes. Math. Scand. 89 (2001), 161-180. DOI 10.7146/math.scand.a-14336 | MR 1868172 | Zbl 1021.13014
[5] L. W. Christensen, H.-B. Foxby: Hyperhomological Algebra with Applications to Commutative Rings. Available at https://www.math.ttu.edu/~lchriste/download/918-final.pdf (2006), 111 pages.
[6] H.-B. Foxby: Bounded complexes of flat modules. J. Pure Appl. Algebra 15 (1979), 149-172. DOI 10.1016/0022-4049(79)90030-6 | MR 0535182 | Zbl 0411.13006
[7] A. Grothendieck: Local Cohomology. Lecture Notes in Mathematics 41. Springer, New York (1967). DOI 10.1007/BFb0073971 | MR 0224620 | Zbl 0185.49202
[8] E. Matlis: The Koszul complex and duality. Commun. Algebra 1 (1974), 87-144. DOI 10.1080/00927877408548611 | MR 0344241 | Zbl 0277.13011
[9] L. Melkersson, P. Schenzel: The co-localization of an Artinian module. Proc. Edinb. Math. Soc., II. Ser. 38 (1995), 121-131. DOI 10.1017/S0013091500006258 | MR 1317331 | Zbl 0824.13011
[10] A. Neeman: The chromatic tower for $D(R)$. Topology 31 (1992), 519-532. DOI 10.1016/0040-9383(92)90047-L | MR 1174255 | Zbl 0793.18008
[11] A. Neeman: Colocalizing subcategories of $D(R)$. J. Reine Angew. Math. 653 (2011), 221-243. DOI 10.1515/crelle.2011.028 | MR 2794632 | Zbl 1221.13030
[12] A. S. Richardson: Co-localization, co-support and local homology. Rocky Mt. J. Math. 36 (2006), 1679-1703. DOI 10.1216/rmjm/1181069391 | MR 2285629 | Zbl 1134.13008
[13] S. Sather-Wagstaff, R. Wicklein: Support and adic finiteness for complexes. Commun. Algebra 45 (2017), 2569-2592. DOI 10.1080/00927872.2015.1087008 | MR 3594539 | Zbl 1386.13046
[14] S. Yassemi: Coassociated primes. Commun. Algebra 23 (1995), 1473-1498. DOI 10.1080/00927879508825288 | MR 1317409 | Zbl 0832.13004

Affiliations: Junquan Qin, Xiaoyan Yang (corresponding author), Department of Mathematics, Northwest Normal University, 967 Anning E. Road, Lanzhou, P. R. China, e-mail: qinjunquan2018@163.com, yangxy@nwnu.edu.cn

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