Is there a way of constructing a morphism between Shimura varieties using differential equations? Maybe, this looks like a completely ridiculous question, so I think that I should explain the context of this question.

In this paper, three related ways of constructing a morphism of Shimura varieties (section 3.1-3.3) are introduced. Among them, the second construction uses realisations of monodromy groups of certain differential equations of second order with coefficients in $\mathbb{C}(z)$ and regular singularities at 0, 1, and $\infty$. I could not find any reference which explains the way of getting (or, finding) such differential equations. Again, I guess that this may be not enough for getting appropriate answer. I am really sorry for failing to ask well-posed question, but this is all I can do since I could not understand any relation between differential equation and Shimura varieties.

Anyone who can introduce related references will be really helpful. Thank you very much in advance.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.