  Here, we study a quantum fermion field in rigid rotation at finite
temperature on anti-de Sitter space. We assume that the rotation rate $\Omega$
is smaller than the inverse radius of curvature $\ell ^{-1}$, so that there is
no speed of light surface and the static (maximally-symmetric) and rotating
vacua coincide. This assumption enables us to follow a geometric approach
employing a closed-form expression for the vacuum two-point function, which can
then be used to compute thermal expectation values (t.e.v.s). In the high
temperature regime, we find a perfect analogy with known results on Minkowski
space-time, uncovering curvature effects in the form of extra terms involving
the Ricci scalar $R$. The axial vortical effect is validated and the axial flux
through two-dimensional slices is found to escape to infinity for massless
fermions, while for massive fermions, it is completely converted into the
pseudoscalar density $-i {\bar \psi} \gamma^5 \psi$. Finally, we discuss
volumetric properties such as the total scalar condensate and the total energy
within the space-time and show that they diverge as $[1 - \ell^2
\Omega^2]^{-1}$ in the limit $\Omega \rightarrow \ell ^{-1}$.
