Representation fields for commutative orders

Details Representation fields for commutative orders Representation fields for commutative orders

2011-04-10

arxiv.org/abs/1104.1809v1

Mathematics

Number Theory

Annales de l'institut Fourier, vol 61, 2011

Scientific paper

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.

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