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We show that any derived equivalent smooth, projective varieties of dimension3 over a finite field $\mathbb{F}_q$ have equal zeta functions. This result isan application of the extension to smooth, projective varieties over any fieldof Popa and Schnell's proof that derived equivalent smooth, projectivevarieties over $\mathbb{C}$ have isogenous Albanese torsors; this result isproven in an appendix by Achter, Casalaina-Martin, Honigs and Vial.

Derived equivalence, Albanese varieties, and the zeta functions of 3-dimensional varieties