Blog

Part I. Say $ K$ is a number field, $ v$ is a finite place of $ K$ , $ K_v$ the $ v$ -adic completion of $ K$ . We have the local Artin map for every finite $ v$ : $ $ \rho_v : K_v^{\times}\to\text{Gal}(K_v^{\rm ab}/K_v)$ $ sending $ \varpi_v$ , a generatorRead more