Galois module

These are representations over a finite field of characteristic ℓ. They often arise as the reduction mod ℓ of an ℓ-adic representation.

There are numerous conditions on representations given by some property of the representation restricted to a decomposition group of some prime. The terminology for these conditions is somewhat chaotic, with different authors inventing different names for the same condition and using the same name with different meanings. Some of these conditions include: