Could you suggest me a book or a link where I can find some information about the Grothendieck problem about differential equations?
The Grothendieck problem that I am reffering to is the following:
$$\alpha_n(x)y^{(n)}(x)+\dots +a_1 (x)y'(x)+a_0(x)y(x)=0, a_i \in \mathbb{Z}[x]\ \ \ \ (*)$$
We suppose that for almost each prime $p$, $(*)$, modulo $p$, has $n$ linearly independent solutions (powerseries in $\mathbb{F}_p((x))$, with field of constants $\mathbb{F}_p((x^p))$). Then $(*)$ has $n$ linearly independent solutions (powerseries in $\mathbb{C}((x))$ with field of constants $\mathbb{C}((x))$) and all are algebraic.