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Mathematical Notes

, Volume 81, Issue 5–6, pp 753–756 | Cite as

On the Brauer group of a two-dimensional local field

  • M. A. Dubovitskaya
Article
  • 39 Downloads

Abstract

The two-dimensional local field K = F q((u))((t)), char K = p, and its Brauer group Br(K) are considered. It is proved that, if L = K(x) is the field extension for which we have x px = ut p =: h, then the condition that (y, f | h]K = 0 for any y ε K is equivalent to the condition f ε Im(Nm(L*)).

Key words

two-dimensional local field Brauer group field extension local field 

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References

  1. 1.
    A. N. Parshin, “Galois cohomology and the Brauer group of local fields,” in Galois Theory, Rings, Algebraic Groups and Their Applications, Trudy Mat. Inst. Steklov (1990), Vol. 183, pp. 159–169 [in Russian].Google Scholar
  2. 2.
    A. N. Parshin, “Local class field theory,” in Algebraic Geometry and Its Applications, Trudy Mat. Inst. Steklov (1984), Vol. 165, pp. 143–170 [in Russian].zbMATHGoogle Scholar
  3. 3.
    J.-P. Serre, Corps Locaux, Deuxième édition. Publications de l’Université de Nancago (Hermann, Paris, 1968), Vol. VIII.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2007

Authors and Affiliations

  • M. A. Dubovitskaya
    • 1
  1. 1.Vavilov Institute for the History of Science and TechnologyRussian Academy of SciencesRussia

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