Ramification groups in Artin-Schreier-Witt extensions
Journal de théorie des nombres de Bordeaux, Tome 17 (2005) no. 2, p. 689-720
Soit K un corps local de caractéristique p>0. L’objectif de cet article est de décrire les groupes de ramification des pro-p extensions abéliennes de K à travers la théorie d’Artin-Schreier-Witt. Dans le cadre usuel de la théorie du corps de classes local, cette étude est menée entièrement et conduit à un accouplement non-dégénéré que nous définissons en détail, généralisant ainsi la formule de Schmid pour les vecteurs de Witt de longueur n. Au passage, on retrouve un résultat de Brylinski avec des arguments plus explicites nécessitant moins d’outils techniques. La dernière partie aborde le cas plus général où le corps résiduel de K est parfait.
Let K be a local field of characteristic p>0. The aim of this paper is to describe the ramification groups for the pro-p abelian extensions over K with regards to the Artin-Schreier-Witt theory. We shall carry out this investigation entirely in the usual framework of local class field theory. This leads to a certain non-degenerate pairing that we shall define in detail, generalizing in this way the Schmid formula to Witt vectors of length n. Along the way, we recover a result of Brylinski but with a different proof which is more explicit and requires less technical machinery. A first attempt is finally made to extend these computations to the case where the perfect field of K is merely perfect.
@article{JTNB_2005__17_2_689_0,
     author = {Thomas, Lara},
     title = {Ramification groups  in Artin-Schreier-Witt extensions},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     publisher = {Universit\'e Bordeaux 1},
     volume = {17},
     number = {2},
     year = {2005},
     pages = {689-720},
     doi = {10.5802/jtnb.514},
     mrnumber = {2211314},
     zbl = {1207.11109},
     language = {en},
     url = {http://http://www.numdam.org/item/JTNB_2005__17_2_689_0}
}
Thomas, Lara. Ramification groups  in Artin-Schreier-Witt extensions. Journal de théorie des nombres de Bordeaux, Tome 17 (2005) no. 2, pp. 689-720. doi : 10.5802/jtnb.514. http://www.numdam.org/item/JTNB_2005__17_2_689_0/

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