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Differential Galois Groups over Laurent Series Fields (1501.06884v1)
Published 27 Jan 2015 in math.AC and math.RA
Abstract: 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).