Parameterized Differential Equations over k((t))(x)

Abstract

In this article, we consider the inverse Galois problem for parameterized differential equations over k((t))(x) with k any field of characteristic zero and use the method of patching over fields due to Harbater and Hartmann. As an application, we prove that every connected semisimple k((t))-split linear algebraic group is a parameterized Galois group over k((t))(x).

13 pages

References in corpus (8)

• Parameterized Picard-Vessiot extensions and Atiyah extensions
• Galois Theory of Parameterized Differential Equations and Linear Differential Algebraic Groups
• Reductive linear differential algebraic groups and the Galois groups of parameterized linear differential equations
• Unipotent differential algebraic groups as parameterized differential Galois groups
• Monodromy groups of parameterized linear differential equations with regular singularities
• A density theorem for parameterized differential Galois theory
• Existence of $\partial$-parameterized Picard-Vessiot extensions over fields with algebraically closed constants
• Local-global principles for torsors over arithmetic curves

Cited by in corpus (1)

• Differential Galois Groups over Laurent Series Fields