Parity and symmetry in intersection and ordinary cohomology
文献类型：期刊论文
| 作者 | Sun, Shenghao1; Zheng, Weizhe2
|
| 刊名 | ALGEBRA & NUMBER THEORY
 |
| 出版日期 | 2016 |
| 卷号 | 10期号:2页码:235-307 |
| 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 |
| ISSN号 | 1937-0652 |
| DOI | 10.2140/ant.2016.10.235 |
| 英文摘要 | 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. |
| 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 |
| 语种 | 英语 |
| WOS记录号 | WOS:000376352000002 |
| 出版者 | MATHEMATICAL SCIENCE PUBL |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/22710]  |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
浏览0
下载0
收藏0
其他版本
除非特别说明，本系统中所有内容都受版权保护，并保留所有权利。