On the integrality of some Galois representations

Abstract:

We find an appropriate topology to put on K, the fraction field of the Iwasawa algebra $\Lambda = {{\mathbf {Z}}_p}[[T]]$, so that compact subgroups of ${K^ \times }$ are in fact contained in ${\Lambda ^ \times }$. This ensures that Galois representations to ${K^ \times }$ have image in ${\Lambda ^ \times }$.