## A dual reciprocity map for local fields |

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### Contents

l Definition of Dual Map | 8 |

2 Main Theorem | 11 |

3 Reciprocity Map Reconstructed | 17 |

Copyright | |

4 other sections not shown

### Common terms and phrases

_is contained abelian extension algebraic algebraic extension Artin and Hasse Artin-Hasse formulas Assume K contains automorphism b s l mod canonical injection Class Field Theory closed subgroup commutative diagram continuous homomorphism Cor(a Cornell University cyclic of order cyclotomic defined defK(a diagram commute Dlog explicit reciprocity laws extension iff finding explicit reciprocity fixed field galois extension galois group ground field group G Hilbert symbols i=peQ inertia subgroup integer isomorphism Iwasawa K/Qp Kummer extensions Let E/K Let tt log cp Math mod I A mod tn modulo norm residue symbol open subgroup p-adic p(GQ pn-primary pn-th root prime prime ideal PROOF Proposition 4b proved ramification index ramified Z extension residue field root of unity s e G satisfies Serre suffices to show Tate 12 Tate's theorem theory of Tate tn-th topology totally ramified unity Cn unramified extension valuation zAnz