Green-Tao theorem in function fields

Abstract

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 $\{f+ Pg : \d(P)<k \}, g \neq 0$.