Lectures «Diophantine Geometry» of Marc Hindry will take place on Mondays since 11.03.2013 at 19:20 in IUM, room 303.
The purpose of the course is to introduce basic tools from algebraic geometry (abelian varieties, line bundles, etc) and algebraic number theory (heights) used in Diophantine Geometry and apply to describe classical theorems of Mordell-Weil : "the group of rational points of an abelian variety is finitely generated" and Faltings : "the set ot rational point of a subvariety of an abelian variety is not Zariski dense (outside trivial cases)".
Program:
- Geometry of curves and algebraic geometry
- Heights (Weil, Nron-Tate, Arakelov)
- Mordell-Weil theorem
- Faltings theorems (sketch)
References:
Lang : Fundamentals of Diophantine Geometry, Springer 1983
Serre : Lectures on the Mordell-Weil theorem, Vieweg 1989
Hindry-Silverman : Diophantine Geometry: an Introduction, Springer 2000
Bombieri-Gubler : Heights in Diophantine Geometry, Cambridge University Press 2006
| 11.03.2013 | |