Displaying similar documents to “On the problem of Baer and Kolchin in the Picard-Vessiot theory”

Reduction of differential equations

Krystyna Skórnik, Joseph Wloka (2000)

Banach Center Publications

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Let (F,D) be a differential field with the subfield of constants C (c ∈ C iff Dc=0). We consider linear differential equations (1) L y = D n y + a n - 1 D n - 1 y + . . . + a 0 y = 0 , where a 0 , . . . , a n ∈ F , and the solution y is in F or in some extension E of F (E ⊇ F). There always exists a (minimal, unique) extension E of F, where Ly=0 has a full system y 1 , . . . , y n of linearly independent (over C) solutions; it is called the Picard-Vessiot extension of F E = PV(F,Ly=0). The Galois group G(E|F) of an extension field E ⊇ F consists of all differential automorphisms...

On the envelope of a vector field

Bernard Malgrange (2011)

Banach Center Publications

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Given a vector field X on an algebraic variety V over ℂ, I compare the following two objects: (i) the envelope of X, the smallest algebraic pseudogroup over V whose Lie algebra contains X, and (ii) the Galois pseudogroup of the foliation defined by the vector field X + d/dt (restricted to one fibre t = constant). I show that either they are equal, or the second has codimension one in the first.

Henselian Discrete Valued Fields Admitting One-Dimensional Local Class Field Theory

Chipchakov, I. (2004)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 11S31 12E15 12F10 12J20. This paper gives a characterization of Henselian discrete valued fields whose finite abelian extensions are uniquely determined by their norm groups and related essentially in the same way as in the classical local class field theory. It determines the structure of the Brauer groups and character groups of Henselian discrete valued strictly primary quasilocal (or PQL-) fields, and thereby, describes the forms...

On the inverse problem of Galois theory.

Núria Vila (1992)

Publicacions Matemàtiques

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The problem of the construction of number fields with Galois group over Q a given finite groups has made considerable progress in the recent years. The aim of this paper is to survey the current state of this problem, giving the most significant methods developed in connection with it.