We will discuss Galois cohomology groups of “intermediate” quotients of an induced module, which sit between Iwasawa cohomology up a tower and cohomology over the ground field. Special elements in Iwasawa cohomology that arise from Euler systems become divisible by a certain Euler factor upon norming down to the ground field. In certain instances, there are reasons to wonder whether this divisibility can also hold for the image in intermediate cohomology. Using “intermediate” Coleman maps, we shall see that the situation locally at $p$ is as nice as one could imagine.