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Large Fields in Differential Galois Theory
- Source :
- J. Inst. Math. Jussieu 20 (2021) 1931-1946
- Publication Year :
- 2017
-
Abstract
- We solve the inverse differential Galois problem over differential fields with a large field of constants of infinite transcendence degree over ${\mathbb Q}$. More generally, we show that over such a field, every split differential embedding problem can be solved. In particular, we solve the inverse differential Galois problem and all split differential embedding problems over ${\mathbb Q}_p(x)$.<br />Comment: 16 pages. Shortened Sections 1 and 2; added Examples 3.2, 3.4, 4.3, 4.5; renumbering of the results in all sections due to these changes
Details
- Database :
- arXiv
- Journal :
- J. Inst. Math. Jussieu 20 (2021) 1931-1946
- Publication Type :
- Report
- Accession number :
- edsarx.1710.03183
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1017/S1474748020000018