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46: 2017/06/28(水)08:33 ID:9bAM9Kta0(1) AA×


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46: [] 2017/06/28(水) 08:33:40 ID:9bAM9Kta0 If a pair d: G→Z^, v: A→Z^ satisfies the class field axiom, then we have the reciprocity low for G, where G is the absolute Galois group of a field k, and A is a continuous multiplicative G module, d is a continuous surjective homomorphism, v is a henselian valuation with respect to d. If k is a local field, we can take A by k*. So now Gal(L/K)^ab is isomorphic to AK / NL/K AL. But in the global case, the situation is more difficult. Considering the appropriate object, we have the n-th power residue resiprocity low for Q. This is a peak which many mathematicians have longed to reach, and of the algebraic number theory. http://lavender.5ch.net/test/read.cgi/hrhm/1466755821/46

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