We will discuss the connection between virtual fibering of surface-by-free groups with the Putman-Wieland conjecture. In particular, we show that there is a surface-by-free group that does not virtually algebraic fiber if and only if a certain part of the Putman-Wieland conjectures holds. We will compare this with similar results in the case of free groups and free-abelian groups. This is joint work with Stefano Vidussi and Genevieve Walsh.
