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Abelian varieties are projective algebraic varieties endowed with an Abelian group structure. Over the complex numbers, they can be described as quotients of a vector space by a lattice of full rank. They are analogs in higher dimensions of elliptic curves, and play an important role in algebraic geometry and number theory.
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When is "independence of l" known?
So maybe everything I'm about to say you already know, so apologies if I'm teaching my grandmother to suck eggs.
This is discussed a bit at the end of a paper of Fontaine "Representations $\ell$-adiq …