Applications of spinor class fields: embeddings of orders and quaternionic lattices

Luis Arenas-Carmona

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Arithmetic of Hermitian forms.

Shimura, Goro (2008)

Documenta Mathematica

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Representation fields for commutative orders

Luis Arenas-Carmona (2012)

Annales de l’institut Fourier

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A representation field for a non-maximal order $ℌ$ 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 $ℌ$ . 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.