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    $\begingroup$ OP has asked specifically about the case of curves, and whether Dwork's proof simplifies in this case. On a brief look, I don't think either of your references addresses that question. $\endgroup$ Commented 10 hours ago
  • $\begingroup$ Chan's thesis might go some way towards that. $\endgroup$ Commented 9 hours ago
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    $\begingroup$ FWIW: My undergraduate thesis fits the category of expository discussions that also, unfortunately, do not meaningfully broach the case of curves. It is linked here. $\endgroup$ Commented 8 hours ago