Geodesic
A categorical approach to Picard-Vessiot theory
Theory and applications of categories, Tome 32 (2017), pp. 488-525

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Picard-Vessiot rings are present in many settings like differential Galois theory, difference Galois theory and Galois theory of Artinian simple module algebras. In this article we set up an abstract framework in which we can prove theorems on existence and uniqueness of Picard-Vessiot rings, as well as on Galois groups corresponding to the Picard-Vessiot rings. As the present approach restricts to the categorical properties which all the categories of differential modules resp.~difference modules etc.~share, it gives unified proofs for all these Galois theories (and maybe more general ones).

Publié le :
Classification : 13B05, 18D10, 12H20
Keywords: Tannakian categories, Picard-Vessiot theory, Galois theory 
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     author = {Andreas Maurischat},
     title = {A categorical approach to {Picard-Vessiot} theory},
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     publisher = {mathdoc},
     volume = {32},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2017_32_a13/}
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Andreas Maurischat. A categorical approach to Picard-Vessiot theory. Theory and applications of categories, Tome 32 (2017), pp. 488-525. http://geodesic.mathdoc.fr/item/TAC_2017_32_a13/