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In geometry, ramification is 'branching out', in the way that the square root function, for complex numbers, can be seen to have two branches differing in sign. The term is also used from the opposite perspective (branches coming together) as when a covering map degenerates at a point of a space, with some collapsing of the fibers of the mapping.
In algebraic number theory, In algebraic topology & In algebra
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ramification displaystyle theory mathfrak algebraic number geometry extensions local complex also field ideal mathcal fields prime analysis numbers one extension
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