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Period-Index, Milnor K-Theory Symbols and Serre's Conjecture II over Dimension-2 Complete Valued Fields

For a complete discretely valued field of dimension 2 with a possibly imperfect residue field, this work proves period equals index for central simple algebras, that every mod-p Milnor K-theory class is a symbol in characteristic 0, and Serre's Conjecture II (triviality of H^1(K,G) for semisimple simply connected G), removing the perfect-residue-field hypothesis of earlier results.

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Central simple algebras, Milnor K-theory and homogeneous spaces over complete discretely valued

Let K be a complete discretely valued field of dimension 2 (for example the completion of a finitely generated field). Prior results on the arithmetic of such fields assumed a perfect residue field; …