Towards explicit description of ramification filtration in the 2-dimensional case

Victor Abrashkin[1]

  • [1] Math. Dept. of Durham University South Road Durham DH7 7QR, United Kingdom & Steklov Math. Institute Gubkina 8, 117966, Moscow, Russia

Journal de Théorie des Nombres de Bordeaux (2004)

  • Volume: 16, Issue: 2, page 293-333
  • ISSN: 1246-7405

Abstract

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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.

How to cite

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Abrashkin, Victor. "Towards explicit description of ramification filtration in the 2-dimensional case." Journal de Théorie des Nombres de Bordeaux 16.2 (2004): 293-333. <http://eudml.org/doc/249248>.

@article{Abrashkin2004,
abstract = {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 $\ge 3$. 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.},
affiliation = {Math. Dept. of Durham University South Road Durham DH7 7QR, United Kingdom & Steklov Math. Institute Gubkina 8, 117966, Moscow, Russia},
author = {Abrashkin, Victor},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {higher dimensional local fields; ramification filtration; upper ramification numbers; local fields},
language = {eng},
number = {2},
pages = {293-333},
publisher = {Université Bordeaux 1},
title = {Towards explicit description of ramification filtration in the 2-dimensional case},
url = {http://eudml.org/doc/249248},
volume = {16},
year = {2004},
}

TY - JOUR
AU - Abrashkin, Victor
TI - Towards explicit description of ramification filtration in the 2-dimensional case
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2004
PB - Université Bordeaux 1
VL - 16
IS - 2
SP - 293
EP - 333
AB - 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 $\ge 3$. 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.
LA - eng
KW - higher dimensional local fields; ramification filtration; upper ramification numbers; local fields
UR - http://eudml.org/doc/249248
ER -

References

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  1. V.A. Abrashkin Ramification filtration of the Galois group of a local field. II. Proceeding of Steklov Math. Inst. 208 (1995). Zbl0884.11047
  2. V.A.AbrashkinRamification filtration of the Galois group of a local field. III. Izvestiya RAN, ser. math. 62, no 5, 3–48. Zbl0918.11060MR1680900
  3. V.A. Abrashkin, On a local analogue of the Grothendieck Conjecture. Intern. Journal of Math. 11 no.1 (2000), 3–43. Zbl1073.12501MR1754618
  4. H. Epp, Eliminating wild ramification. Invent. Math. 19 (1973), 235–249. Zbl0254.13008MR321929
  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. Zbl0428.12013MR550688
  6. Sh. Mochizuki, A version of the Grothendieck conjecture for p -adic local fields. Int. J. Math. 8 no. 4 (1997), 499–506. Zbl0894.11046MR1460898
  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. Zbl0579.12012MR752939
  8. J.-P. Serre, Corps locaux. Hermann, Paris, 1968. Zbl0137.02601MR354618
  9. I. Zhukov, On ramification theory in the imperfect residue field case. Preprint of Nottingham University 98-02 (1998). 

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