Oriented right-angled Artin pro-l groups and maximal pro-l Galois groups

For a prime number ℓ we introduce and study oriented right-angled Artin pro-ℓ groups GΓ,λ(oriented pro-ℓ RAAGs for short) associated to a finite oriented graph Γ and a continuous group homomorphism λ:Zℓ→Z×ℓ. We show that an oriented pro-ℓ RAAG GΓ,λ is a Bloch-Kato pro-ℓ group if, and only if, (GΓ,λ,θΓ,λ) is an oriented pro-ℓ group of elementary type generalizing a recent result of I. Snopche and P. Zalesskii. Here θΓ,λ:GΓ,λ→Z×p denotes the canonical ℓ-orientation on GΓ,λ. We invest some effort in order to show that oriented right-angled Artin pro-ℓ groups share many properties with right-angled Artin pro-ℓ-groups or even discrete RAAG's, e.g., if Γ is a specially oriented chordal graph, then GΓ,λ is coherent, generalizing a result of C. Droms. Moreover, in this case (GΓ,λ,θΓ,λ) has the Positselski-Bogomolov property generalizing a result of H. Servatius, C. Droms and B. Servatius for discrete RAAG's. If Γ is a specially oriented chordal graph and Im(λ)⊆1+4Z2 in case that ℓ=2, then H∙(GΓ,λ,Fℓ)≃Λ∙(Γ¨op) generalizing a well known result of M. Salvetti.