Grunwald–wang for Global Character Groups
نویسنده
چکیده
Let F denote C or Q` for a prime ` 6= char(k), equipped with its natural topology, and let Gk = Gal(ks/k) for a choice of separable closure ks/k. For each place v of k choose a separable closure kv,s/kv and an embedding ks ↪→ kv,s over k ↪→ kv, thereby identifying Gkv with a decomposition group at v in Gk. It is surprising (but confirmed by consultation with experts) that the following natural local-to-global question for F×-valued characters (always
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