Birch–Tate conjecture
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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 2011.
[edit] References
- J. T. Tate, Symbols in Arithmetic, Actes, Congrès Intern. Math., Nice, 1970, Tome 1, Gauthier–Villars(1971), 201–211
[edit] External links
- Hurrelbrink, J. (2001), "Birch–Tate conjecture", in Hazewinkel, Michiel, Encyclopedia of Mathematics, Springer, ISBN 978-1556080104, http://www.encyclopediaofmath.org/index.php?title=Birch%E2%80%93Tate_conjecture
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