Parity and symmetry in intersection and ordinary cohomology

doi:10.2140/ant.2016.10.235

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	Parity and symmetry in intersection and ordinary cohomology
	Sun, Shenghao 1; Zheng, Weizhe2
	2016
发表期刊	ALGEBRA & NUMBER THEORY
ISSN	1937-0652
卷号	10 期号:2 页码:235-307
摘要	We show that the Galois representations provided by l-adic cohomology of proper smooth varieties, and more generally by l-adic intersection cohomology of proper varieties, over any field, are orthogonal or symplectic according to the degree. We deduce this from a preservation result of orthogonal and symplectic pure perverse sheaves by proper direct image. We show, moreover, that the subgroup of the Grothendieck group generated by orthogonal pure perverse sheaves of even weights and symplectic pure perverse sheaves of odd weights are preserved by Grothendieck's six operations. Over a finite field, we deduce parity and symmetry results for Jordan blocks appearing in the Frobenius action on intersection cohomology of proper varieties, and virtual parity results for the Frobenius action on ordinary cohomology of arbitrary varieties.
关键词	l-adic cohomology intersection cohomology Galois representation symmetric form alternating form pure perverse sheaf decomposition theorem horizontal complex alteration Deligne-Mumford stack Grothendieck-Witt group
DOI	10.2140/ant.2016.10.235
语种	英语
资助项目	ANR grant G-FIB ; China's Recruitment Program of Global Experts ; National Natural Science Foundation of China[11321101] ; National Center for Mathematics and Interdisciplinary Sciences ; Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000376352000002
出版者	MATHEMATICAL SCIENCE PUBL
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/22711
专题	数学所
通讯作者	Sun, Shenghao; Zheng, Weizhe
作者单位	1.Tsinghua Univ, Yau Math Sci Ctr, Jinchunyuan West Bldg, Beijing 100084, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Morningside Ctr Math, Zhongguancun Donglu 55, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Sun, Shenghao,Zheng, Weizhe. Parity and symmetry in intersection and ordinary cohomology[J]. ALGEBRA & NUMBER THEORY,2016,10(2):235-307.
APA	Sun, Shenghao,&Zheng, Weizhe.(2016).Parity and symmetry in intersection and ordinary cohomology.ALGEBRA & NUMBER THEORY,10(2),235-307.
MLA	Sun, Shenghao,et al."Parity and symmetry in intersection and ordinary cohomology".ALGEBRA & NUMBER THEORY 10.2(2016):235-307.