The completion problem for equivariant K-theory

被引：5
作者：
Krishna, Amalendu [1 ]
机构：
[1] Tata Inst Fundamental Res, Sch Math, 1 Homi Bhabha Rd, Bombay 400005, Maharashtra, India
来源：
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK | 2018年 / 740卷
关键词：
RIEMANN-ROCH; CHOW GROUPS; COBORDISM; COHOMOLOGY; SCHEMES;
D O I：
10.1515/crelle-2015-0063
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we study the Atiyah-Segal completion problem for the equivariant algebraic K-theory. We show that this completion problem has a positive solution for the action of connected groups on smooth projective schemes. In contrast, we show that this problem has a negative solution for non-projective smooth schemes, even if the action has only finite stabilizers.
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收藏
页码：275 / 317
页数：43
相关论文
共 43 条
[1]  
[Anonymous], 2013, GRADUATE STUDIES MAT
[2]  
ARTIN M, 1969, LECT NOTES MATH, V100
[3]  
Atiyah MF, 1969, J. Differential Geometry, V3, P1
[4]  
Atiyah MF, 1961, P S PURE MATH, V3, P7
[5]   THEOREMS ON ACTIONS OF ALGEBRAIC GROUPS [J].
BIALYNIC.A .
ANNALS OF MATHEMATICS, 1973, 98 (03) :480-497
[6]  
Borel A., 1991, GRAD TEXTS MATH, V8
[7]  
Brion M., 1997, Journal of Transformation Groups, V2, P225, DOI [10.1007/BF01234659, DOI 10.1007/BF01234659]
[8]   Voevodsky's Lectures on Motivic Cohomology 2000/2001 [J].
Deligne, Pierre .
ALGEBRAIC TOPOLOGY: THE ABEL SYMPOSIUM 2007, 2009, 4 :355-409
[9]  
Edidin D, 1998, INVENT MATH, V131, P595, DOI 10.1007/s002220050214
[10]  
Edidin D, 2000, DUKE MATH J, V102, P567
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