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- W4295172820 abstract "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 $Omega=k[![G]!]$ 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 unital $A_{infty}$-modules $D_{infty}(bigwedge frak{g}^{vee})$. In the case where $G$ is an abelian group we prove that the $A_{infty}$-structure is trivial and deduce an equivalence between $D(Omega)$ and the derived category of differential graded modules over $bigwedge frak{g}^{vee}$ which generalizes a result of Schneider for $Bbb{Z}_p$." @default.
- W4295172820 created "2022-09-11" @default.
- W4295172820 creator A5016334318 @default.
- W4295172820 date "2019-02-25" @default.
- W4295172820 modified "2023-10-18" @default.
- W4295172820 title "Koszul duality for Iwasawa algebras modulo p" @default.
- W4295172820 doi "https://doi.org/10.48550/arxiv.1902.09632" @default.
- W4295172820 hasPublicationYear "2019" @default.
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