Terkko Navigator / Arithmetic geometry : lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, September 10-15, 2007

These notes fall into two parts. The first part, which goes up to the end of Sect. 5, is a general survey of some of the topics in the theory of Diophantine equations which interest me and on which I hope to see progress within the next 10 years.

Voici une série de résultats classiques. Toute forme quadratique en au moins trois variables sur le corps fini$$\mathbb{F}_p$$(p premier)possède un zéro non trivial (Euler).

Beginning with the work of Osgood [65], it has been known that the branch of complex analysis known as Nevanlinna theory (also called value distribution theory) has many similarities with Roth’s theorem on diophantine approximation.