Compatible system of ℓ-adic representations
- Compatible system of ℓ-adic representations
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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. Prototypical examples include the cyclotomic character and the Tate module of an abelian variety. 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[1] 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.
Notes
References
- Serre, Jean-Pierre (1998) [1968], 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 978-1-568-81077-5, MR1484415
- Taylor, Richard (2004), "Galois representations", Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série 6 13 (1): 73–119, MR2060030
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