Pure Picard-Vessiot extensions with generic properties

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Abstract

Given a connected linear algebraic group G over an algebraically closed field C of characteristic 0, we construct a pure Picard-Vessiot extension for G, namely, a Picard-Vessiot extension ε ⊃ ℱ, with differential Galois group G, such that ε and ℱ are purely differentially transcendental over C. The differential field ε is the quotient field of a G-stable proper differential subring ℛ with the property that if F is any differential field with field of constants C and E ⊃ F is a Picard-Vessiot extension with differential Galois group a connected subgroup H of G, then there is a differential homomorphism ø: ℛ → E such that E is generated over F as a differential field by ø(ℛ).

Original languageEnglish
Pages (from-to)2549-2556
Number of pages8
JournalProceedings of the American Mathematical Society
Volume132
Issue number9
DOIs
StatePublished - Sep 2004

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