Splitting theorem (splittingtheorem) The theorem to determine the splitting of prime ideals in the category domain theory. If K/k is the category domain of H, where H is the subgroup containing k'of the Idal group J* of k, Then any prime divisor v of k is completely split in K if and only if kvCH, where k2 is the completeness of k to v. Furthermore, there are the following results: if K/k is any Abelian expansion, v Is any prime divisor of k, then the image of the elements in kv under the Ating map is exactly the decomposition group Gv (that is, the Galois group of Kw/k two, w is any continuation of v in k). , And more
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