In algebraic number theory, the Gras conjecture relates the ''p''-parts of the Galois eigenspaces of an

ideal class group In number theory, the ideal class group (or class group) of an algebraic number field is the quotient group where is the group of fractional ideals of the ring of integers of , and is its subgroup of principal ideals. The class group is a mea ...

to the group of global units modulo cyclotomic units. It was proved by as a corollary of their work on the

main conjecture of Iwasawa theory In mathematics, the main conjecture of Iwasawa theory is a deep relationship between ''p''-adic ''L''-functions and ideal class groups of cyclotomic fields, proved by Kenkichi Iwasawa for primes satisfying the Kummer–Vandiver conjecture and ...

. later gave a simpler proof using

Euler system In mathematics, an Euler system is a collection of compatible elements of Galois cohomology groups indexed by fields. They were introduced by in his work on Heegner points on modular elliptic curves, which was motivated by his earlier paper and ...

References

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