Gras conjecture

In algebraic number theory, the Gras conjecture relates the p-parts of the Galois eigenspaces of an ideal class group 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. later gave a simpler proof using Euler systems. A version of the Gras conjecture applying to ray class groups was later proven by Timothy All.