Existence of ∂-parameterized Picard-Vessiot extensions over fields with algebraically closed constants

2011/04/18 by Michael Wibmer, Wibmer, Michael · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #12H05 #12H10 #Advanced Differential Equations and Dynamical Systems #Commutative Algebra (math.AC) #FOS: Mathematics #Nonlinear Waves and Solitons #Polynomial and algebraic computation #math.AC #msc:12H05 #msc:12H10

paper · pdf · doi:10.48550/arxiv.1104.3514

13 pages

arxiv created 2011/04/18 · openalex publication_date 2011/04/18 · arxiv updated 2011/04/19 · openalex created_date 2022/08/29 · openalex updated_date 2026/07/28

Abstract

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

Citations

• Difference Nullstellensatz in the case of finite group
• A Chevalley theorem for difference equations
• Descent for differential Galois theory of difference equations. Confluence and q-dependency

Cited by

• Galois theories for q-difference equations: comparison theorems

Related

• Picard--Vessiot structures
• Real Picard-Vessiot theory
• Picard-Vessiot theory for real partial differential fields
• Embedded Picard-Vessiot extensions
• The Complete Picard Vessiot Closure