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- W4366400465 abstract "For a prime number $ell$ we introduce and study oriented right-angled Artin pro-$ell$ groups $G_{Gamma,lambda}$(oriented pro-$ell$ RAAGs for short) associated to a finite oriented graph $Gamma$ and a continuous group homomorphism $lambdacolonmathbb Z_elltomathbb Z_ell^times$. We show that an oriented pro-$ell$ RAAG $G_{Gamma,lambda}$ is a Bloch-Kato pro-$ell$ group if, and only if, $(G_{Gamma,lambda},theta_{Gamma,lambda})$ is an oriented pro-$ell$ group of elementary type generalizing a recent result of I. Snopche and P. Zalesskii. Here $theta_{Gamma,lambda}colon G_{Gamma,lambda}tomathbb Z_p^times$ denotes the canonical $ell$-orientation on $G_{Gamma,lambda}$. We invest some effort in order to show that oriented right-angled Artin pro-$ell$ groups share many properties with right-angled Artin pro-$ell$-groups or even discrete RAAG's, e.g., if $Gamma$ is a specially oriented chordal graph, then $G_{Gamma,lambda}$ is coherent, generalizing a result of C. Droms. Moreover, in this case $(G_{Gamma,lambda},theta_{Gamma,lambda})$ has the Positselski-Bogomolov property generalizing a result of H. Servatius, C. Droms and B. Servatius for discrete RAAG's. If $Gamma$ is a specially oriented chordal graph and ${rm Im}(lambda)subseteq 1+4mathbb Z_2$ in case that $ell=2$, then ${rm H}^bullet(G_{Gamma,lambda},mathbb F_ell) simeq Lambda^bullet(ddot{Gamma}^{rm op})$ generalizing a well known result of M. Salvetti." @default.
- W4366400465 created "2023-04-21" @default.
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- W4366400465 date "2023-04-17" @default.
- W4366400465 modified "2023-10-18" @default.
- W4366400465 title "Oriented right-angled Artin pro-$ell$ groups and maximal pro-$ell$ Galois groups" @default.
- W4366400465 doi "https://doi.org/10.48550/arxiv.2304.08123" @default.
- W4366400465 hasPublicationYear "2023" @default.
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