A matroid is GF(q)-regular if it is representable over all proper superfields of the field GF(q). We show that, for highly connected matroids having a large projective geometry over GF(q) as a minor, the property of GF(q)-regularity is equivalent to representability over both GF(q) and GF(q) for some odd integer t ≥ 3. We do this by means of an exact… (More)