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Valuations and Differential Galois Groups
ISBN-13:
9781470406158
Einband:
PDF
Seiten:
68
Autor:
Guillaume Duval
eBook Typ:
PDF
eBook Format:
PDF
Kopierschutz:
Adobe DRM [Hard-DRM]
Sprache:
Deutsch
Beschreibung:
In this paper, valuation theory is used to analyse infinitesimal behaviour of solutions of linear differential equations. For any Picard-Vessiot extension $(F / K, partial)$ with differential Galois group $G$, the author looks at the valuations of $F$ which are left invariant by $G$. The main reason for this is the following: If a given invariant valuation $u$ measures infinitesimal behaviour of functions belonging to $F$, then two conjugate elements of $F$ will share the same infinitesimal behaviour with respect to $u$. This memoir is divided into seven sections.
In this paper, valuation theory is used to analyse infinitesimal behaviour of solutions of linear differential equations. For any Picard-Vessiot extension $(F / K, partial)$ with differential Galois group $G$, the author looks at the valuations of $F$ which are left invariant by $G$. The main reason for this is the following: If a given invariant valuation $u$ measures infinitesimal behaviour of functions belonging to $F$, then two conjugate elements of $F$ will share the same infinitesimal behaviour with respect to $u$. This memoir is divided into seven sections.