2011/04/10 by Arenas-Carmona, Luis
#FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.1104.1809
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.