Abelian l-Adic Representations and Elliptic Curves

This work reproduces a series of lectures held at McGill University in 1967. It presents the idele-theoretic approach to Abelian representations, particularly those that arise from the modules of ln-th division points of elliptic curves.

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This classic book contains an introduction to systems of l-adic representations, a topic of great importance in number theory and algebraic geometry, as reflected by the spectacular recent developments on the Taniyama-Weil conjecture and Fermat's Last Theorem. The initial chapters are devoted to the Abelian case (complex multiplication), where one finds a nice correspondence between the l-adic representations and the linear representations of some algebraic groups (now called Taniyama groups). The last chapter handles the case of elliptic curves with no complex multiplication, the main result of which is that the image of the Galois group (in the corresponding l-adic representation) is "large."