Compatible system of ℓ-adic representations
In number theory, a compatible system of ℓ-adic representations is an abstraction of certain important families of ℓ-adic Galois representations, indexed by prime numbers ℓ, that have compatibility properties for almost all ℓ.
A slightly more restrictive notion is that of a strictly compatible system of ℓ-adic representations which offers more control on the compatibility properties. More recently, some authors have started requiring more compatibility related to p-adic Hodge theory.
Compatible systems of ℓ-adic representations are a fundamental concept in contemporary algebraic number theory.
- Such as Taylor 2004
- Serre, Jean-Pierre (1998) , Abelian l-adic representations and elliptic curves, Research Notes in Mathematics, 7, with the collaboration of Willem Kuyk and John Labute, Wellesley, MA: A K Peters, ISBN 978-1-56881-077-5, MR 1484415