Existence of $\partial$-parameterized Picard-Vessiot extensions over fields with algebraically closed constants

Abstract

The purpose of this short note is to establish the existence of $\partial$-parameterized Picard-Vessiot extensions of systems of linear difference-differential equations over difference-differential fields with algebraically closed constants.

13 pages

References in corpus (5)

• The inverse problem of differential Galois theory over the field R(z)
• Difference Nullstellensatz in the case of finite group
• A Chevalley theorem for difference equations
• Difference Nullstellensatz
• Descent for differential Galois theory of difference equations. Confluence and q-dependency

Cited by in corpus (6)

• Reductive linear differential algebraic groups and the Galois groups of parameterized linear differential equations
• A Galois-theoretic proof of the differential transcendence of the incomplete Gamma function
• Computation of the unipotent radical of the differential Galois group for a parameterized second-order linear differential equation
• Parameterized Differential Equations over k((t))(x)
• Descent for differential Galois theory of difference equations. Confluence and q-dependency
• Linear Algebraic Groups as Parameterized Picard-Vessiot Galois Groups