Cohomological Hasse principle and resolution of quotient singularities

被引:0
作者
Kerz, Moritz [1 ]
Saito, Shuji [2 ]
机构
[1] Univ Regensburg, NWF I Math, D-93040 Regensburg, Germany
[2] Tokyo Inst Technol, Grad Sch Sci & Engn, Interact Res Ctr Sci, Meguro, Tokyo 1528551, Japan
来源
NEW YORK JOURNAL OF MATHEMATICS | 2013年 / 19卷
关键词
resolution of singularities; Hasse principle; TORIC SINGULARITIES; CHARACTERISTIC ZERO; K-THEORY; VARIETIES; FACTORIZATION; COMPLEXES; DESCENT; MAPS;
D O I
暂无
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this paper we study weight homology of singular schemes. Weight homology is an invariant of a singular scheme defined in terms of hypercoverings of resolution of singularities. Our main result is a McKay principle for weight homology of quotient singularities, i.e., we describe weight homology of a quotient scheme in terms of weight homology of an equivariant scheme. Our method is to reduce the geometric McKay principle for weight homology to Kato's cohomological Hasse principle for arithmetic schemes. The McKay principle for weight homology implies the McKay principle for the homotopy type of the dual complex of the exceptional divisors of a resolution of a quotient singularity. As a consequence we show that the dual complex is contractible for isolated quotient singularities.
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页码:597 / 645
页数:49
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