Bloch-Kato groups over perfectoid fields and Galois theory of $p$-adic
periods
Bloch-Kato groups over perfectoid fields and Galois theory of $p$-adic
periods
We relate the structure of the Bloch-Kato groups associated with a de Rham Galois representation over a perfectoid field to the Galois theory of the ring $\mathbf{B}_\mathrm{dR}^+$ of $p$-adic periods. As an application, we answer the question raised by Coates and Greenberg and motivated by Iwasawa theory to compute the …