To Shenghao: reference on Shimura varieties of PEL type

[张庆]

Dear Shenghao:

I am reading Milne's notes "Introduction to Shimura varieties" and Deligne's paper "Travaux de Shimura".

I want to know more about the shimura varieties of PEL type, including the canonical model is the moduli space of abelian varieties with additional structure. Milne's notes only mention the complex points of the shimura varieties classify these abelian varieties. Milne mentioned in his notes that he follows the unpublished version of Deligne's "Travaux de Shimura", but I cannot find the unpublished version.

He also mentioned Zink's and Kottwitz's paper, but Zink's paper was written in Germany and Kottwitz's paper "Points on some Shimura varieties over finite fields" seems to be difficult for me.

So I want to ask if any other references written in English or French about this topic exsit, and it is better to includes more details about the representability of the functor.  

Best regards,

 

Zhang Qing

[tt]

You can find more about PEL Shimura varieties in Lan, Kaiwen's thesis.

Milne has many good papers on canonical models of Shimura varieties,
available on his webpage. The "Introduction to ..." is a course note.