Anogia Summer school, July 23–29, 2005
Number fields and curves over finite fields
Preliminary Program:
- Robin de Jong: In this lecture series we will
discuss the basic notions and ideas
of Arakelov theory for curves over a number field. We will see how
Arakelov theory gives rise to some interesting arithmetic invariants.
We will study some explicit examples of these invariants and we
we will show how certain bounds for these invariants imply the
Mordell conjecture.
Literature.
- Michael Tsfasman: The title is Asymptotic
theory of global fields. We will relate the
contents of the papers
Infinite global fields and the generalized Brauer-Siegel theorem
(pdf) and
Asymptotic behaviour of the Euler-Kronecker constant
(pdf)
- Gerard van der Geer: Curves over finite fields and
modular forms. In these lectures we discuss curves and abelian varieties
over finite fields. After discussing the basics we intend to show how counting
curves over finite fields can be used to obtain information about modular
forms.
- René Schoof: In these lectures we present classical
algebraic number theory from the point of view of Arakelov theory.
We discuss the relations between Arakelov divisors and ideal lattices
and applications to fast algorithms to compute Arakelov
class groups (Buchmann's algorithm, infrastructure).
See [1], [2].