Splitting fields of differential symbol algebras

Abstract

For m >= 2, we study derivations on symbol algebras of degree m over fields with characteristic not dividing m. A differential central simple algebra over a field k is split by a finitely generated extension of k. For certain derivations on symbol algebras, we provide explicit construction of differential splitting fields and give bounds on their algebraic and transcendence degrees. We further analyze maximal subfields that split certain differential symbol algebras.