We prove that the SU(2) Witten–Reshetikhin–Turaev invariant of any 3-manifold with any colored link inside at any root of unity is an algebraic integer. As a byproduct, we get a new proof of the integrality of the SO(3) Witten–Reshetikhin–Turaev invariant for any 3-manifold with any colored link inside at any root of unity of odd order.
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Anna Beliakova, Qi Chen, Thang T. Q. Lê, On the integrality of the Witten–Reshetikhin–Turaev 3-manifold invariants. Quantum Topol. 5 (2014), no. 1, pp. 99–141