## Galois cohomology in Dedekind domains |

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### Contents

2 Some exact sequences in cohomology of finite | 15 |

3 An annihilator of l Galois cohomology in | 20 |

Bibliography | 29 |

### Common terms and phrases

A-homomorphism AnnA(M annihilated by tt B/BQ bG/H Cauchy sequence cohomology of finite Colombia component-wise contained Corollary coset decomposition G cup product decomposition group Dedekind domain defined deflation map denote direct products divisor q element of Q elements q epimorphism expressing the cohomology extension L/K field of fractions finite Galois extension finite groups follows G-A module G-regular GALOIS COHOMOLOGY Galois group group of G groups H G H G,B H_l(G,B Hi(G homomorphism of G/H-modules integer i H integral closure isomorphic Let us consider long exact sequence Marco Fidel Suarez Mathematics Moreover non-zero prime ideals Proof Proposition 3*l Proposition l.l3 proved that VL q in L/K q in Q Q lying q q aq q-adic completion quotient group r/Pn ramification filtration ramification index res(A(a residue field characteristic ring of integers SG/H tamely ramified Theorem l.3 VL/VK