Representation fields for commutative orders
Abstract
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.
- Publication:
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arXiv e-prints
- Pub Date:
- April 2011
- DOI:
- 10.48550/arXiv.1104.1809
- arXiv:
- arXiv:1104.1809
- Bibcode:
- 2011arXiv1104.1809A
- Keywords:
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- Mathematics - Number Theory
- E-Print:
- Annales de l'institut Fourier, vol 61, 2011