Green-Tao theorem in function fields

We adapt the proof of the Green-Tao theorem on arithmetic progressions in primes to the setting of polynomials over a finite field, to show that for every $k$, the irreducible polynomials in ${\mathbf{F}}_q[t]$ contain configurations of the form $\{f+Pg:\text{d}(P)<k\},g\mathrm{\ne }0$.