Remote Access St. Petersburg Mathematical Journal

St. Petersburg Mathematical Journal

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

Request Permissions   Purchase Content 
 

 

Independent generators of the $ K$-group of a standard two-dimensional field


Author: O. Yu. Ivanova
Translated by: N. B. Lebedinskaya
Original publication: Algebra i Analiz, tom 26 (2014), nomer 4.
Journal: St. Petersburg Math. J. 26 (2015), 567-592
MSC (2010): Primary 20G25
DOI: https://doi.org/10.1090/spmj/1351
Published electronically: May 6, 2015
MathSciNet review: 3289186
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: It is proved that the $ K$-group of any standard two-dimensional field possesses a system of independent generators. Sufficient conditions for generators to be independent are obtained. For a certain class of fields, such generators are described explicitly.


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

  • 1. S. V. Vostokov, Explicit construction of the theory of class fields of a multidimensional local field, Izv. Akad. Nauk SSSR Ser. Mat. 49 (1985), no. 2, 283–308, 461 (Russian). MR 791304
  • 2. I. Zhukov, Milnor and topological 𝐾-groups of higher-dimensional complete fields, Algebra i Analiz 9 (1997), no. 1, 98–147 (Russian); English transl., St. Petersburg Math. J. 9 (1998), no. 1, 69–105. MR 1458420
  • 3. O. Yu. Ivanova, Orders of topological generators of the 𝐾-groups of a standard two-dimensional local field, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 356 (2008), no. Voprosy Teorii Predstavleniĭ Algebr i Grupp. 17, 118–148, 190 (Russian, with English and Russian summaries); English transl., J. Math. Sci. (N.Y.) 156 (2009), no. 6, 918–936. MR 2760367, https://doi.org/10.1007/s10958-009-9298-1
  • 4. I. B. Fesenko, Theory of local fields. Local class field theory. Multidimensional local class field theory, Algebra i Analiz 4 (1992), no. 3, 1–41 (Russian, with Russian summary); English transl., St. Petersburg Math. J. 4 (1993), no. 3, 403–438. MR 1190770
  • 5. I. B. Fesenko and S. V. Vostokov, Local fields and their extensions, Translations of Mathematical Monographs, vol. 121, American Mathematical Society, Providence, RI, 1993. A constructive approach; With a foreword by I. R. Shafarevich. MR 1218392
  • 6. Ivan Fesenko, Topological Milnor 𝐾-groups of higher local fields, Invitation to higher local fields (Münster, 1999) Geom. Topol. Monogr., vol. 3, Geom. Topol. Publ., Coventry, 2000, pp. 61–74. MR 1804920, https://doi.org/10.2140/gtm.2000.3.61
  • 7. Hiroo Miki, On 𝑍_{𝑝}-extensions of complete 𝑝-adic power series fields and function fields, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 21 (1974), 377–393. MR 0364206
  • 8. A. A. Suslin, Torsion in 𝐾₂ of fields, 𝐾-Theory 1 (1987), no. 1, 5–29. MR 899915, https://doi.org/10.1007/BF00533985

Similar Articles

Retrieve articles in St. Petersburg Mathematical Journal with MSC (2010): 20G25

Retrieve articles in all journals with MSC (2010): 20G25


Additional Information

O. Yu. Ivanova
Affiliation: St. Petersburg State University of Aerospace Engineering, Bol′shaya Morskaya str. 67, St. Petersburg 190000, Russia
Email: olgaiv80@mail.ru

DOI: https://doi.org/10.1090/spmj/1351
Keywords: Local fields, two-dimensional fields, $K$-groups
Received by editor(s): June 10, 2013
Published electronically: May 6, 2015
Additional Notes: Supported by RFBR (grant no. 11-01-00588-a)
Article copyright: © Copyright 2015 American Mathematical Society