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 $\mathbb{Q}_{p}(x)$.

中文翻译：

---

微分伽罗瓦理论中的大域

我们解决了微分域上的逆微分伽罗瓦问题，该域具有无限超越度的大常数域$\mathbb{Q}$. 更一般地说，我们表明，在这样一个领域，每个分裂差分嵌入问题都可以解决。特别是，我们解决了逆微分伽罗瓦问题和所有分裂微分嵌入问题$\mathbb{Q}_{p}(x)$.