# Arithmetic of number fields, the geometry of algebraic curves and Nevanlinna theory (1st Dec, 2010 - 31st Jan, 2011)

Arithmetic of number fields, the geometry of algebraic curves and Nevanlina theory: analogies and differences. similarity between the degree of line bundles and divisor, the arakelov degree and The Nevanlinna counting function (I will give the definitions). The first Main theorem of Nevanlinna theory, the Poincare' Lelong formula and the arithmetic analogue. Introduction to the arithmetic of foliations. Proof of the one dimensional case of geometric version of Schneider Lang theorem. ... as A background I will assume some general knowledge of Algebraic geometry: (Hartshorne book level) and some some general knowledge of Dedekind rings (first chapters of Lang "algebraic number theory" or first chapters of Serre "Local Fields"), the notion of non archimedean field is necessary.

### Schedule of lectures for December can be found here