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


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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  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
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    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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