3 problems

Let $K$ be any real number field and let ${\mathcal H}_K$ be its $p$-class group, of exponent $p^{e(K)}$. For any prime number $\ell \equiv 1 \pmod {2p^N}$, with $N \geq e(K)$, let…

Let $K$ be any totally real number field, let $p$ be a prime, and let ${\mathcal H}_K$ be its $p$-class group of exponent $p^e$. For an integer $N\geq e$, consider primes $\ell$ sa…

Principal capitulation conjecture. The order of the capitulation kernel is a multiple of the degree of the extension: