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Titlebook: Galois Theory of Linear Differential Equations; Marius Put,Michael F. Singer Book 2003 Springer-Verlag Berlin Heidelberg 2003 Arithmetic.A

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书目名称Galois Theory of Linear Differential Equations
编辑Marius Put,Michael F. Singer
视频video
概述Includes supplementary material:
丛书名称Grundlehren der mathematischen Wissenschaften
图书封面Titlebook: Galois Theory of Linear Differential Equations;  Marius Put,Michael F. Singer Book 2003 Springer-Verlag Berlin Heidelberg 2003 Arithmetic.A
描述.Linear differential equations form the central topic of this volume, Galois theory being the unifying theme..A large number of aspects are presented: algebraic theory especially differential Galois theory, formal theory, classification, algorithms to decide solvability in finite terms, monodromy and Hilbert‘s 21st problem, asymptotics and summability, the inverse problem and linear differential equations in positive characteristic. The appendices aim to help the reader with concepts used, from algebraic geometry, linear algebraic groups, sheaves, and tannakian categories that are used. .This volume will become a standard reference for all mathematicians in this area of mathematics, including graduate students..
出版日期Book 2003
关键词Arithmetic; Asymptotics; Computer Algebra; Direct Problems; Galois Theory; Global Classification; Inverse
版次1
doihttps://doi.org/10.1007/978-3-642-55750-7
isbn_softcover978-3-642-62916-7
isbn_ebook978-3-642-55750-7Series ISSN 0072-7830 Series E-ISSN 2196-9701
issn_series 0072-7830
copyrightSpringer-Verlag Berlin Heidelberg 2003
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Darstellung: Gewinn- & Verlust-Profile,ver .({.})) quasi-split equation δ−. that is isomorphic, over .((.)), to δ−. (cf. Proposition 3.41). This means that there is a . such that .. In the following, δ−., δ−., and . are fixed and the eigenvalues of δ−., δ−. are denoted by .,…, ..
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Picard-Vessiot Theoryor all of this material can be found in the classics of Kaplansky [151] and Kolchin [162] (and Kolchin’s original papers that have been collected in [25]) as well as the recent book of Magid [183] and the papers [231] and [173].
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Stokes Phenomenon and Differential Galois Groupsver .({.})) quasi-split equation δ−. that is isomorphic, over .((.)), to δ−. (cf. Proposition 3.41). This means that there is a . such that .. In the following, δ−., δ−., and . are fixed and the eigenvalues of δ−., δ−. are denoted by .,…, ..
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Stokes Matrices and Meromorphic Classification with a differential module . a triple Trip(.)=(., {.}, γ). More precisely, a tannakian category Gr. was defined, which has as objects the above triples. The functor Trip: . from the category of the differential modules over . to the category of triples was shown to be an equivalence of tannakian categories.
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Positive Characteristics conjecture on .-curvatures is one of the motivations for this. Another motivation is the observation that for the factorization of differential operators over, say, the differential field Q(.) the reductions modulo prime numbers yield useful information.
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