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What's the current state of the Breuil-Mezard conjecture? Has the original version (from the 2002 paper) been solved in its entirety? What are some of the new directions being explored?

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    $\begingroup$ have you checked out On the Breuil-Mézard conjecture ?-- it's a 2015 paper, so I would think that gives the state of the art... $\endgroup$
    – Carlo Beenakker
    Commented Feb 14, 2018 at 3:39
  • $\begingroup$ I saw that paper, but I wanted to hear about the generalizations for the n-dimensional case. Also, in the 2-dimensional case, there seem to be some minor conditions placed on the representation, so I wanted someone to clarify that as well. $\endgroup$
    – Hodge-Tate
    Commented Feb 14, 2018 at 23:48

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