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On the classification of 3-dimensional non-associative division algebras over p -adic fields

Abdulaziz DeajimDavid Grant — 2011

Journal de Théorie des Nombres de Bordeaux

Let p be a prime and K a p -adic field (a finite extension of the field of p -adic numbers p ). We employ the main results in [12] and the arithmetic of elliptic curves over K to reduce the problem of classifying 3-dimensional non-associative division algebras (up to isotopy) over K to the classification of ternary cubic forms H over K (up to equivalence) with no non-trivial zeros over K . We give an explicit solution to the latter problem, which we...

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