TL;DR
This paper proves the existence and uniqueness of Picard--Vessiot extensions for linear differential systems over certain fields, using a model theoretic approach, including cases over real fields with real-closed constants.
Contribution
It introduces a model theoretic method to establish existence and uniqueness of Picard--Vessiot extensions under specific field conditions, expanding previous algebraic results.
Findings
Existence of Picard--Vessiot extensions under closure assumptions.
Uniqueness of these extensions in the specified setting.
Application to real fields with real-closed constants.
Abstract
We demonstrate existence and uniqueness of Picard--Vessiot extensions satisfying prescribed properties, for systems of linear differential equations over a field satisfying the same properties, under some closure assumptions on the field of constants. An example includes the case of a equations over a real field, with a real-closed field of constants. The result is obtained through a model theoretic approach.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsProteoglycans and glycosaminoglycans research · Homotopy and Cohomology in Algebraic Topology · Polynomial and algebraic computation