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Representation fields for commutative orders
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
Roots of unity in definite quaternion orders
A commutative order in a quaternion algebra is called selective if it is
embeds into some, but not all, the maximal orders in the algebra. It is known
that a given quadratic order over a number field can be selective in at most
one indefinite quaternion algebra. Here we prove that the order generated by a
cubic root of unity is selective for any definite quaternion algebra over the
rationals with a type number 3 or larger. The proof extends to a few other
closely related orders
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