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Totally ramified extensions October 23, 2009

Posted by Akhil Mathew in algebra, algebraic number theory, number theory.
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Today we consider the case of a totally ramified extension of local fields {K \subset L}, with residue fields {\overline{K}, \overline{L}}—recall that this means {e=[L:K]=n,f=1}. It turns out that there is a similar characterization as for unramified extensions. (more…)