On weight complexes, pure functors, and detecting weights

被引:5
作者
Bondarko, Mikhail, V
机构
基金
俄罗斯科学基金会;
关键词
Triangulated category; Weight structure; Weight complex; Weight-exact functor; Conservativity; Motives; Pure functors; Equivariant stable homotopy category; Mackey functors; Bredon cohomology; T-STRUCTURES; MOTIVES; CATEGORIES; RESOLUTION;
D O I
10.1016/j.jalgebra.2021.02.005
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
This paper is dedicated to the study of weight complex functors (defined on triangulated categories endowed with weight structures) and their applications. We introduce pure(co)homological functors that "ignore all non-zero weights"; these have a nice description in terms of weight complexes. An important example is the weight structure wGgenerated by the orbit category in the G-equivariant stable homotopy category SH(G); the corresponding pure cohomological functors into abelian groups are the Bredon cohomology associated to Mackey functors ones. Pure functors related to "motivic" weight structures are also quite useful. Our results also give some (more) new weight structures. Moreover, we prove that certain exact functors are conservative and "detect weights". (C) 2021 Elsevier Inc. All rights reserved.
引用
收藏
页码:617 / 668
页数:52
相关论文
共 50 条
[1]  
André Y, 2002, REND SEMIN MAT U PAD, V108, P107
[2]  
[Anonymous], 1975, Ann. Sci. Ecole Norm. Sup. 4
[3]  
[Anonymous], 2017, Hodge theory and L2-analysis, Adv. Lect. Math. (ALM)
[4]  
[Anonymous], 1995, IMRN, DOI 10.1155/S1073792895000158
[5]  
Ayoub J, 2018, TOPOLOGIE FEUILLETEE
[6]  
Bachmann T, 2017, DOC MATH, V22, P363
[7]   Idempotent completion of triangulated categories [J].
Balmer, P ;
Schlichting, M .
JOURNAL OF ALGEBRA, 2001, 236 (02) :819-834
[8]  
Barr M, 2005, THEOR APPL CATEG, V14, P53
[9]  
BEILINSON AA, 1982, ASTERISQUE, P7
[10]   A DG guide to Voevodsky's motives [J].
Beilinson, Alexander ;
Vologodsky, Vadim .
GEOMETRIC AND FUNCTIONAL ANALYSIS, 2008, 17 (06) :1709-1787