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Section 3.8 - Higher Direct Images of Sheaves

In this note we study the higher direct image functors Rf∗(−) and the higher coinverse image functors Rf (−) which will play a role in our study of Serre duality. The main theorem is the proof that if F is quasi-coherent then so is Rf∗(F ), which we prove first for noetherian schemes and then more generally for quasi-compact quasi-separated schemes. Most proofs are from either Hartshorne’s book [1] or Kempf’s paper [2], with some elaborations.