Compactification des vari\'et\'es de Deligne-Lusztig
  We construct explicitly the normalisation of the Bott-Samelson-Demazure-Hansen compactification of Deligne-Lusztig varieties $X(w)$ in their covering $Y(w)$: we retrieve a result by Deligne-Lusztig about the local monodromy around the divisors of the compactification. 
C\'edric Bonnaf\'e (LM-Besan\c{c}on), Rapha\"el Rouquier (MI)