Rational points on 3-folds with nef anti-canonical class over finite fields

We prove that a geometrically integral smooth projective 3-fold (Formula presented.) with nef anti-canonical class and negative Kodaira dimension over a finite field (Formula presented.) of characteristic (Formula presented.) and cardinality (Formula presented.) has a rational point. Additionally, under the same assumptions on (Formula presented.) and (Formula presented.), we show that a smooth projective 3-fold (Formula presented.) with trivial canonical class and non-zero first Betti number (Formula presented.) has a rational point. Our techniques rely on the Minimal Model Program to establish several structure results for generalized log Calabi–Yau 3-fold pairs over perfect fields.