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- W2937456841 abstract "Let $X$ be a smooth scheme over an algebraically closed field. When $X$ is proper, it was proved in cite{me1} that the moduli of $ell$-adic continuous representations of $pi_1^et(X)$, $LocSys(X)$, is representable by a (derived) $Ql$-analytic space. However, in the non-proper case one cannot expect that the results of cite{me1} hold mutatis mutandis. Instead, assuming $ell$ is invertible in $X$, one has to bound the ramification at infinity of those considered continuous representations. The main goal of the current text is to give a proof of such representability statements in the open case. We also extend the representability results of cite{me1}. More specifically, assuming $X$ is assumed to be proper, we show that $LocSys(X)$ admits a canonical shifted symplectic form and we give some applications of such existence result." @default.
- W2937456841 created "2019-04-25" @default.
- W2937456841 creator A5058374259 @default.
- W2937456841 date "2019-04-16" @default.
- W2937456841 modified "2023-09-27" @default.
- W2937456841 title "Moduli of $ell$-adic pro-'etale local systems for smooth non-proper schemes." @default.
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