A representation field for a non-maximal order \Ha in a central simple
algebra is a subfield of the spinor class field of maximal orders which
determines the set of spinor genera of maximal orders containing a copy of
\Ha. Not every non-maximal order has a representation field. In this work we
prove that every commutative order has a representation field and give a
formula for it. The main result is proved for central simple algebras over
arbitrary global fields.Comment: Annales de l'institut Fourier, vol 61, 201
