  In this manuscript, we apply patching methods to give a positive answer to
the inverse differential Galois problem over function fields over Laurent
series fields of characteristic zero. More precisely, we show that any linear
algebraic group (i.e. affine group scheme of finite type) over such a Laurent
series field does occur as the differential Galois group of a linear
differential equation with coefficients in any such function field (of one or
several variables).

Commutative Algebra;Rings and Algebras