Algebraic Function Fields

Abstract Riemann surfaces. Valuations. Local methods. Newton’s polygon. Differentials. Theorem of residues. Adeles. Riemann-Roch theorem. Hurwitz’ formula. Elliptical and hyperelliptical functions. Weierstrass points. Very ample divisors. Non-singular algebraic curves. Compact Riemann surfaces.

References:
CHEVALLEY, C. – Introduction to the Theory of Algebraic Functions of One Variable, New York, AMS Math. Surveys, 1951.
DEURING, M. – Lecture on the Theory of Algebraic Functions of One Variable. Berlin, Springer-Verlag, Lectures Notes in Mathematics, 314, 1973.
LANG, S. – Introduction to Algebraic and Abelian Functions, 2nd ed., Reading, Mass., Addison-Wesley, New York, Springer-Verlag, 1982.
STICHTENOTH, H. – Algebraic Function Fields and Codes, New York, Springer-Verlag, 1993.

* Standard program. The teacher has the autonomy to make any changes