Stratifying triangulated categories

被引：59

作者：

Benson, Dave ^{[1
]}

Iyengar, Srikanth B. ^{[2
]}

Krause, Henning ^{[3
]}

机构：

[1] Univ Aberdeen, Kings Coll, Inst Math, Aberdeen AB24 3UE, Scotland

[2] Univ Nebraska, Dept Math, Lincoln, NE 68588 USA

[3] Univ Paderborn, Inst Math, D-33095 Paderborn, Germany

来源：

JOURNAL OF TOPOLOGY | 2011年 / 4卷 / 03期

基金：

美国国家科学基金会;

关键词：

FINITE-GROUP SCHEMES; SUPPORT VARIETIES; COHOMOLOGY; MODULES; SUBCATEGORIES; BOUSFIELD; ALGEBRAS; THEOREM; RING;

D O I：

10.1112/jtopol/jtr017

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A notion of stratification is introduced for any compactly generated triangulated category T endowed with an action of a graded-commutative noetherian ring R. The utility of this notion is demonstrated by establishing diverse consequences that follow if T is stratified by R. Among them are a classification of the localizing subcategories of T in terms of subsets of the set of prime ideals in R; a classification of the thick subcategories of the subcategory of compact objects in T; and results on the support of the graded R-module of morphisms Hom(T)*(C, D) leading to analogs of the tensor product theorem for support varieties of modular representation of groups.

引用

页码：641 / 666

页数：26

共 31 条

[11] Dimensions of triangulated categories via Koszul objects [J].

Bergh, Petter Andreas ;

Iyengar, Srikanth B. ;

Krause, Henning ;

Oppermann, Steffen .

MATHEMATISCHE ZEITSCHRIFT, 2010, 265 (04) :849-864

[12]

BOKSTEDT M, 1993, COMPOS MATH, V86, P209

[13] THE VARIETIES AND THE CO-HOMOLOGY RING OF A MODULE [J].

CARLSON, JF .

JOURNAL OF ALGEBRA, 1983, 85 (01) :104-143

[14] Support varieties for selfinjective algebras [J].

Erdmann, Karin ;

Holloway, Miles ;

Taillefer, Rachel ;

Snashall, Nicole ;

Solberg, Oyvind .

K-THEORY, 2004, 33 (01) :67-87

[15] SUPPORT VARIETIES FOR RESTRICTED LIE-ALGEBRAS [J].

FRIEDLANDER, EM ;

PARSHALL, BJ .

INVENTIONES MATHEMATICAE, 1986, 86 (03) :553-562

[16] Representation-theoretic support spaces for finite group schemes [J].

Friedlander, EM ;

Pevtsova, J .

AMERICAN JOURNAL OF MATHEMATICS, 2005, 127 (02) :379-420

[17] Π-supports for modules for finite group schemes [J].

Friedlander, Eric M. ;

Pevtsova, Julia .

DUKE MATHEMATICAL JOURNAL, 2007, 139 (02) :317-368

[18]

Gabriel P., 1967, Ergebnisse der Mathematik und ihrer Grenzgebiete, V35

[19]

Hopkins M. J., 1987, London Math. Soc. Lecture Note Ser., V117, P73

[20]

Hovey Mark, 1997, MEM AM MATH SOC, V128, pX+114, DOI [10.1090/memo/0610, DOI 10.1090/MEMO/0610]

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