Birch–Tate conjecture explained
The Birch–Tate conjecture is a conjecture in mathematics (more specifically in algebraic K-theory) proposed by both Bryan John Birch and John Tate.
Statement
. More specifically, let
F be a
totally real number field and let
N be the largest natural number such that the
extension of
F by the
Nth
root of unity has an
elementary abelian 2-group as its
Galois group. Then the conjecture states that
Status
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."
References
- J. T. Tate, Symbols in Arithmetic, Actes, Congrès Intern. Math., Nice, 1970, Tome 1, Gauthier–Villars(1971), 201–211
