当前位置: X-MOL 学术Adv. Math. › 论文详情
Equivariant localization and completion in cyclic homology and derived loop spaces
Advances in Mathematics ( IF 1.435 ) Pub Date : 2020-02-03 , DOI: 10.1016/j.aim.2020.107005
Harrison Chen

We prove an equivariant localization theorem over an algebraically closed field of characteristic zero for smooth quotient stacks by reductive groups X/G in the setting of derived loop spaces as well as Hochschild homology and its cyclic variants. We show that the derived loop spaces of the stack X/G and its classical z-fixed point stack π0(Xz)/Gz become equivalent after completion along a semisimple parameter [z]∈G//G, implying the analogous statement for Hochschild and cyclic homology of the dg category of perfect complexes Perf(X/G). We then prove an analogue of the Atiyah-Segal completion theorem in the setting of periodic cyclic homology, where the completion of the periodic cyclic homology of Perf(X/G) at the identity [e]∈G//G is identified with a 2-periodic version of the derived de Rham cohomology of X/G. Together, these results identify the completed periodic cyclic homology of a stack X/G over a parameter [z]∈G//G with the 2-periodic derived de Rham cohomology of its z-fixed points.
更新日期:2020-02-03

 

全部期刊列表>>
化学/材料学中国作者研究精选
Springer Nature 2019高下载量文章和章节
《科学报告》最新环境科学研究
ACS材料视界
自然科研论文编辑服务
中南大学国家杰青杨华明
剑桥大学-
中国科学院大学化学科学学院
材料化学和生物传感方向博士后招聘
课题组网站
X-MOL
北京大学分子工程苏南研究院
华东师范大学分子机器及功能材料
中山大学化学工程与技术学院
试剂库存
天合科研
down
wechat
bug