Large Fields in Differential Galois Theory

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 ${\mathbb{Q}}_p(x)$.

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

References in corpus (1)

• Differential Galois Groups over Laurent Series Fields

Cited by in corpus (1)

• Differentially Large Fields