Birch–Tate conjecture

Birch–Tate conjecture

The Birch–Tate conjecture is based on algebraic K-theory proposed by both Bryan John Birch and John Tate. It relates the value of a Dedekind zeta function at s = −1 to the order of K2 of the ring of integers, for a number field F.

Progress on this conjecture has been made as a consequence of work on Iwasawa theory, and in particular of the proofs given for the so-called "main conjecture of Iwasawa theory."

The problem remains unsolved as of 2006.


  • J. T. Tate, Symbols in Arithmetic, Actes, Congrès Intern. Math., Nice, 1970, Tome 1, Gauthier–Villars(1971), 201–211

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