I'm interested in coherent sheaves on a singular curve.(For example, global dimension, Serre duality, Riemann-Roch's theorem for singular curves,etc....) I find treatment of it only in Hartshorn's exercises. Are there general treatments of singular curves? And are there good references of singular curves?

  • $\begingroup$ Try to look into Burban, Igor; Kreußler, Bernd Derived categories of irreducible projective curves of arithmetic genus one. Compos. Math. 142 (2006), no. 5, 1231–1262. $\endgroup$ – Sasha Feb 12 at 15:58
  • $\begingroup$ Serre's book: Groupes alge'briques et corps de classes, or Algebraic Groups and Class Fields, chapter IV, is a standard reference. $\endgroup$ – roy smith Feb 15 at 22:27

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