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Titlebook: Introduction to Algebraic and Abelian Functions; Serge Lang Textbook 19822nd edition Springer-Verlag New York Inc 1982 Abelsche Funktion.A

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The Riemann-Roch Theorem,We recall that a . . is a principal ideal ring (and therefore a unique factorization ring) having only one prime. If . is a generator of this prime, we call . a ..
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The Riemann Surface,The purpose of this chapter is to show how to give a structure of analytic manifold to the set of points on a curve in the complex numbers, but our treatment also applies to more general fields like .-adic numbers. We are principally interested in the complex case, in order to derive the Abel-Jacobi theorem in the next chapter.
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The Theorem of Abel-Jacobi,A differential will be said to be of the . if it is holomorphic everywhere on the Riemann surface. Such differentials form a vector space over the complex, and by the Riemann-Roch theorem, one sees that the dimension of this space is equal to the genus . of ..
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