I was wondering if somebody could give me a quick primer on Honda-Tate theory, specifically the number of isogeny classes of elliptic curves, and how specifically it's utilized in (Scholze's refinement of) the Langlands-Kottwitz method.

I realize this is not a "good question" and may be poorly received, but I do believe such an answer would be very helpful to students (and even researchers) interested in the work of Scholze here.

Thanks!