examples of ramification of archimedean places
Let be a CM-field i.e. is a totally imaginary (http://planetmath.org/TotallyRealAndImaginaryFields) quadratic extension of a totally real field . Then we claim that the extension is totally ramified at the archimedean (or infinite) places. Indeed, let be an archimedean place of . By assumption, is a totally real field, thus all its places are real, and so, is real. Let be any archimedean place of lying above (i.e. extending to ). Since is totally imaginary, the place is a pair of complex embeddings, and therefore ramifies in . Thus, all archimedean places of ramify in and for all .
|Title||examples of ramification of archimedean places|
|Date of creation||2013-03-22 15:07:29|
|Last modified on||2013-03-22 15:07:29|
|Last modified by||alozano (2414)|