Vendredi 09 octobre 2020
Marine Rougnant
(Université de Franche-Comté)
What can be said about about the behaviour of a prime 
along a fields extension of a given field 
? After a brief presentation of ramification theory and pro- groups, we will see that the notion of -rationality arises naturally when looking at the maximal pro- extension 
of unramified outside : is said to be -rational when the Galois group 
is pro- free.
Recently, Gras conjectured that a fixed field is -rational for large . We will see that the generalized abc-conjecture brings a first step toward the question of quantifying -rational fields in low degree.