Résumé : Ramification theory for local fields becomes complicated when the residue field is no longer required to be perfect. I will describe two approaches in the case of equal characteristic : one introduced by Abbes and Saito, involving geometry of some rigid spaces in equal characteristic, and a second approach using p-adic differential equations on some rigid spaces in mixed characteristic. I will also give a very brief discussion of some recent work of my student Liang Xiao, who has shown that these approaches give identical results. (While this statement is true both at the level of Artin conductors and Swan conductors, for this talk I will stick to the Artin case.)
Lieu : bât. 425 - 113-115
Département de Mathématiques
Bâtiment 307
Faculté des Sciences d'Orsay Université Paris-Sud F-91405 Orsay Cedex Tél. : +33 (0) 1-69-15-79-56 
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