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arXiv · 0812.2433

On the Dec group of finite abelian Galois extensions over global fields

Jean B Nganou
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Abstract

If K/F is a finite abelian Galois extension of global fields whose Galois group has exponent t, we prove that there exists a short exact sequence that has as a consequence that if t is square free, then Dec(K/F)=Br_{t}(K/F) which we use to show that prime exponent division algebras over Henselian valued fields with global residue fields are isomorphic to a tensor product of cyclic algebras. Finally, we construct a counterexample to the result for higher exponent division algebras.

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Jean B Nganou. 2008-12-12. On the Dec group of finite abelian Galois extensions over global fields. https://arxiv.org/abs/0812.2433

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