Remote Access St. Petersburg Mathematical Journal

St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)

Request Permissions   Purchase Content 
 

 

Approximation approach to ramification theory


Authors: I. B. Zhukov and G. K. Pak
Translated by: I. B. Zhukov
Original publication: Algebra i Analiz, tom 27 (2015), nomer 6.
Journal: St. Petersburg Math. J. 27 (2016), 967-976
MSC (2010): Primary 11S15; Secondary 14E22
DOI: https://doi.org/10.1090/spmj/1429
Published electronically: September 30, 2016
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A new approach is suggested to the theory of ramification in finite extensions of complete discrete valuation fields in the case of an imperfect residue field. It is based on the notion of a distance between extensions that shows the difference in ramification depths arising after a base change of a certain type. For two-dimensional local fields of prime characteristic, the following is proved. If the distance between two constant extensions (i.e., extensions defined over a given field with perfect residue field) is zero, then the corresponding Hasse-Herbrand functions coincide. The converse is verified only for extensions of degree $ p$.


References [Enhancements On Off] (What's this?)

  • 1. L. Xiao and I. Zhukov, Ramification of higher local fields, approaches and questions, Algebra i Analiz 26 (2014), no. 5, 1–63; English transl., St. Petersburg Math. J. 26 (2015), no. 5, 695–740. MR 3408704
  • 2. Liang Xiao and Igor Zhukov, Ramification of higher local fields, approaches and questions [reprint of MR3408704], Valuation theory in interaction, EMS Ser. Congr. Rep., Eur. Math. Soc., Zürich, 2014, pp. 600–656. MR 3329050
  • 3. I. B. Zhukov, Ramification in elementary abelian extensions, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 413 (2013), no. Voprosy Teorii Predstavleniĭ Algebr i Grupp. 24, 106–114, 229 (Russian, with English and Russian summaries); English transl., J. Math. Sci. (N.Y.) 202 (2014), no. 3, 404–409. MR 3073060
  • 4. -, The elementary abelian conductor, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 423 (2014), 126-131; English transl., J. Math. Sci. (N.Y.) 209 (2015), no. 4, 564-567.
  • 5. I. B. Zhukov and M. V. Koroteev, Elimination of wild ramification, Algebra i Analiz 11 (1999), no. 6, 153–177 (Russian); English transl., St. Petersburg Math. J. 11 (2000), no. 6, 1063–1083. MR 1746073
  • 6. I. B. Zhukov, On ramification theory in the case of an imperfect residue field, Mat. Sb. 194 (2003), no. 12, 3–30 (Russian, with Russian summary); English transl., Sb. Math. 194 (2003), no. 11-12, 1747–1774. MR 2052694, https://doi.org/10.1070/SM2003v194n12ABEH000785

Similar Articles

Retrieve articles in St. Petersburg Mathematical Journal with MSC (2010): 11S15, 14E22

Retrieve articles in all journals with MSC (2010): 11S15, 14E22


Additional Information

I. B. Zhukov
Affiliation: Department of Mathematics and Mechanics, St. Petersburg State University, Universitetskiĭ pr. 28, Petrodvorets, St. Petersburg 198504, Russia
Email: i.zhukov@spbu.ru

G. K. Pak
Affiliation: Institute of Mathematics and Computer Science, Far-East State University, Oktyabr′skaya ul. 27, 690000 Vladivostok, Russia
Email: pakgk@imcs.dvgu.ru

DOI: https://doi.org/10.1090/spmj/1429
Keywords: Higher local fields, ramification, imperfect residue field
Received by editor(s): September 1, 2015
Published electronically: September 30, 2016
Additional Notes: Supported by RFBR (grant no. 14-01-00393-a)
Dedicated: to Sergey Vladimirovich Vostokov with deep gratitude
Article copyright: © Copyright 2016 American Mathematical Society