Towards explicit description of ramification filtration in the 2-dimensional case
Journal de Théorie des Nombres de Bordeaux, Tome 16 (2004) no. 2, pp. 293-333.

Le résultat principal de cet article est une description explicite de la structure des sous-groupes de ramification du groupe de Galois d’un corps local de dimension 2 modulo son sous-groupe des commutateurs d’ordre 3. Ce résultat joue un role clé dans la preuve par l’auteur d’un analogue de la conjecture de Grothendieck pour les corps de dimension supérieure, cf. Proc. Steklov Math. Institute, vol.  241, 2003, pp.  2-34.

The principal result of this paper is an explicit description of the structure of ramification subgroups of the Galois group of 2-dimensional local field modulo its subgroup of commutators of order 3. This result plays a clue role in the author’s proof of an analogue of the Grothendieck Conjecture for higher dimensional local fields, cf. Proc. Steklov Math. Institute, vol.  241, 2003, pp.  2-34.

@article{JTNB_2004__16_2_293_0,
     author = {Victor Abrashkin},
     title = {Towards explicit description of ramification filtration in the 2-dimensional case},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {293--333},
     publisher = {Universit\'e Bordeaux 1},
     volume = {16},
     number = {2},
     year = {2004},
     doi = {10.5802/jtnb.448},
     zbl = {02188519},
     mrnumber = {2143556},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.448/}
}
Victor Abrashkin. Towards explicit description of ramification filtration in the 2-dimensional case. Journal de Théorie des Nombres de Bordeaux, Tome 16 (2004) no. 2, pp. 293-333. doi : 10.5802/jtnb.448. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.448/

[1] V.A. Abrashkin Ramification filtration of the Galois group of a local field. II. Proceeding of Steklov Math. Inst. 208 (1995). | Zbl 0884.11047

[2] V.A.Abrashkin Ramification filtration of the Galois group of a local field. III. Izvestiya RAN, ser. math. 62, no 5, 3–48. | MR 1680900 | Zbl 0918.11060

[3] V.A. Abrashkin, On a local analogue of the Grothendieck Conjecture. Intern. Journal of Math. 11 no.1 (2000), 3–43. | MR 1754618 | Zbl 1073.12501

[4] H. Epp, Eliminating wild ramification. Invent. Math. 19 (1973), 235–249. | MR 321929 | Zbl 0254.13008

[5] K. Kato, A generalisation of local class field theory by using K-groups I. J. Fac. Sci. Univ. Tokyo Sec. IA 26 no.2 (1979), 303–376. | MR 550688 | Zbl 0428.12013

[6] Sh. Mochizuki, A version of the Grothendieck conjecture for p-adic local fields. Int. J. Math. 8 no. 4 (1997), 499–506. | MR 1460898 | Zbl 0894.11046

[7] A.N. Parshin, Local class field theory. Trudy Mat. Inst. Steklov 165 (1984) English transl. in Proc.Steklov Math. Inst. 165 (1985) 157–185. | MR 752939 | Zbl 0579.12012

[8] J.-P. Serre, Corps locaux. Hermann, Paris, 1968. | MR 354618 | Zbl 0137.02601

[9] I. Zhukov, On ramification theory in the imperfect residue field case. Preprint of Nottingham University 98-02 (1998).