Levels and sublevels of composition algebras over mathfrakpmathfrak{p}-adic function fields

摘要

In [7], the level and sublevel of composition algebras are studied, wherein these quantities are determined for those algebras defined over local fields. In this paper, the level and sublevel of composition algebras, of dimension 4 and 8 over rational function fields over local non-dyadic fields, are determined completely in terms of the local ramification data of the algebras. The proofs are based on the “classification” of quadratic forms over such fields, as is given in [8].