By Fred Diamond,Jerry Shurman

This booklet introduces the speculation of modular varieties, from which all rational elliptic curves come up, with an eye fixed towards the Modularity Theorem. dialogue covers elliptic curves as advanced tori and as algebraic curves; modular curves as Riemann surfaces and as algebraic curves; Hecke operators and Atkin-Lehner conception; Hecke eigenforms and their mathematics homes; the Jacobians of modular curves and the Abelian forms linked to Hecke eigenforms. because it provides those rules, the publication states the Modularity Theorem in quite a few types, bearing on them to one another and concerning their purposes to quantity idea. The authors think no historical past in algebraic quantity thought and algebraic geometry. routines are included.

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