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# Aurlien Galateau

(Universit Paris-Sud)
## Elliptic curves and Serre's "big image" theorem

Миникурс будет проходить на факультете математики НИУ ВШЭ (ул.
Вавилова, д.7) по средам, начиная с 31.10.2012 в 15:30 в аудитории 311-312.
### Аннотация курса

The course will be an introduction to the theory of elliptic curves,
with a view toward Serre's work on the Galois representations attached
to their torsion. We will start with a geometric description
(projective embedding, group law, isogenies, endomorphism ring) and
then focus on the case of elliptic curves defined over finite fields
(Hasse's estimate, ordinary and supersingular curves) and local fields
(reduction, Nron-Ogg-Shafarevich criterion). Next, we will explain
the link between complex multiplication (CM) on elliptic curves and
class field theory of imaginary quadratic fields. The last part of the
course will be devoted to non-CM elliptic curves and the Galois
properties of their torsion points.