Milnor k-group attached to a torus and birch-tate conjecture

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2 Citations (Scopus)


We formulate (and prove under a certain assumption) a conjecture relating the order of Somekawa's Milnor K-group attached to a torus T and the value of the Artin L-function attached to the cocharacter group of T (regarded as an Artin representation) at s = -1. The case T = m reduces to the classical BirchTate conjecture.

Original languageEnglish
Pages (from-to)841-857
Number of pages17
JournalInternational Journal of Mathematics
Issue number7
Publication statusPublished - 2009 Jul


  • Artin L-function
  • Birch-Tate conjecture
  • Milnor K-groups attached to tori

ASJC Scopus subject areas

  • Mathematics(all)


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