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What are some derived schemes naturally arising in geometric representation theory? Some examples include:

  • Steinberg scheme
  • Hilbert scheme
  • Moduli stack of local systems.

Now, this looks like a community wiki question to me so maybe it should be marked as such.

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    $\begingroup$ What do you call a derived scheme? $\endgroup$
    – abx
    Commented Feb 13, 2019 at 20:57
  • $\begingroup$ either the definition in simplicial context or connective spectral context (and stacks are allowed too) $\endgroup$
    – paul
    Commented Feb 14, 2019 at 3:20
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    $\begingroup$ Opening "On two geometric realizations of an affine Hecke algebra" by Bezrukavnikov, or most recent papers by Gaitsgory should give a good supply :) I also found Mirkovic-Riche "Linear Koszul duality" rather beautiful ... innocent enough, but the idea is very nice. $\endgroup$
    – Geordie Williamson
    Commented Feb 14, 2019 at 10:03

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