Koszul duality for Iwasawa algebras modulo $p$
作者: Claus Sorensen
刊名: Representation Theory of the American Mathematical Society, 2020, Vol.24 (5), pp.151-177
来源数据库: American Mathematical Society Journal
DOI: 10.1090/ert/539
原始语种摘要: In this article we establish a version of Koszul duality for filtered rings arising from $ p$-adic Lie groups. Our precise setup is the following. We let $ G$ be a uniform pro-$ p$ group and consider its completed group algebra $ \Omega =k\llbracket G\rrbracket $ with coefficients in a finite field $ k$ of characteristic $ p$. It is known that $ \Omega $ carries a natural filtration and $ \text {gr} \Omega =S(\frak {g})$ where $ \frak {g}$ is the (abelian) Lie algebra of $ G$ over $ k$. One of our main results in this paper is that the Koszul dual $ \text {gr} \Omega ^!=\bigwedge \frak {g}^{\vee }$ can be promoted to an $ A_{\infty }$-algebra in such a way that the derived category of pseudocompact $ \Omega $-modules $ D(\Omega )$ becomes equivalent to the derived category of strictly...
全文获取路径: AMS 

  • Omega 希腊字母的最后一字(Ω,ω)奥米伽(导航系统)希腊字母的末一字
  • duality 二重性
  • algebra 代数学
  • prove 实验
  • consider 仔细考虑
  • derived 导生的
  • category 
  • group 
  • natural 自然的
  • modulo