By Jean-Pierre Serre

This vintage publication includes an advent to platforms of l-adic representations, a subject matter of significant value in quantity idea and algebraic geometry, as mirrored via the stunning fresh advancements at the Taniyama-Weil conjecture and Fermat's final Theorem. The preliminary chapters are dedicated to the Abelian case (complex multiplication), the place one reveals a pleasant correspondence among the l-adic representations and the linear representations of a few algebraic teams (now referred to as Taniyama groups). The final bankruptcy handles the case of elliptic curves with out complicated multiplication, the most results of that is that identical to the Galois team (in the corresponding l-adic illustration) is "large."

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