algebraic number theory Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations. Number-theoretic questions are expressed in terms of properties of algebraic ob ...

, the Gras conjecture relates the ''p''-parts of the Galois eigenspaces of an ideal class group to the group of global units modulo

cyclotomic unit In mathematics, a cyclotomic unit (or circular unit) is a unit (ring theory), unit of an algebraic number field which is the product of numbers of the form (ζ − 1) for ζ an ''n''th root of unity and 0 < ''a'' < ''n''.

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s. It was proved by as a corollary of their work on the main conjecture of Iwasawa theory. later gave a simpler proof using Euler systems.

References

* * * Theorems in algebraic number theory Conjectures that have been proved {{numtheory-stub