The lectures take place on Tuesday at
and on Friday at (local time).
Some lecture notes
(handwritten, in French) from last year are available.
Normal xtensions, separables extensions
()
Primitive element theorem, perfect fields, Artin's theorem
()
Galois extensions, Galois correspondence, Galois group of
,
Galois theory of finite fields
()
Existence of polynomials with Galois group
,
for
prime, irreductibility and action of the Galois group, cyclotomic extensions,
is algebraically closed, constructions with (ruler and) compass
()
Constructions with (ruler and) compass
(list of constructions with a compass),
constructible regular polygons, linear independance of characters
()
Normal basis theorem, trace and norm
()
Trace form, group cohomology
(
and
), restriction, inflation, (co-)induced module, Shapiro's lemma
()
Shapiro's lemma (end of proof), corestriction, cohomology exact sequence,
Galois cohomology, Hilbert 90, application to Pythagorean triples
()
Cyclic extensions, Artin-Shreier extensions, Kummer theory
()
Kummer theory, resolubility of a polynomial equation
()
Non finite Galois extensions, Krull topology,
Artin's theorem, Galois correspondence for non finite extensions
()
Absolute Galois group of a field, étale algebras over a field, classification
()
Equivalence between the category of finite étale algebras over a field
and finite sets with an action of the absolute Galois group, factorisation
of ideals in number fields
()
Action of the Galois group on a factorization, decomposition group,
inertia group, ramification
()