Abstract
Let K denote any differential field such that its field of constants C={a∈K|a′=0} is algebraically closed, has characteristic 0 and is different from K. The neutral tannakian category Diff K of differential modules over K is equivalent to the category Repr H of all finite dimensional representations (over C) of some affine group scheme H over C (see Appendices B.2 and B.3 for the definition and properties). Let C be a full subcategory of Diff K that is closed under all operations of linear algebra, i.e., kernels, cokernels, direct sums, and tensor products. Then C is also a neutral tannakian category and equivalent to Repr G for some affine group scheme G.
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© 2003 Springer-Verlag Berlin Heidelberg
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van der Put, M., Singer, M.F. (2003). Universal Picard-Vessiot Rings and Galois Groups. In: Galois Theory of Linear Differential Equations. Grundlehren der mathematischen Wissenschaften, vol 328. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55750-7_10
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DOI: https://doi.org/10.1007/978-3-642-55750-7_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-62916-7
Online ISBN: 978-3-642-55750-7
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