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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!

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    $\begingroup$ The application of Honda-Tate theory to point counting goes back at least to Kottwitz himself. Scholze's main insight has little do with this, but rather with noticing that it is possible to compute the nearby cycle cohomology of modular curves at primes of bad reduction via point counting on models with good reduction, and via a general theorem about nearby cycles for regular schemes. In any case, there are somewhat legible notes on the topic here: fields.utoronto.ca/programs/scientific/11-12/galoisrep/… $\endgroup$
    – Keerthi Madapusi
    Commented Mar 29, 2017 at 4:09
  • $\begingroup$ Sorry, I phrased my question poorly. I've edited what I've said in light of what you said @KeerthiMadapusiPera. $\endgroup$
    – Anonymous Google Document Anim
    Commented Mar 29, 2017 at 21:35

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