The Rising Sea

Notes Update

March 27, 2006 on 9:58 pm | In Note Updates | No Comments

Nothing of great excitement in this month’s notes update. I’ve made some minor additions and changes to existing notes:

• Derived Categories of Quasi-coherent Sheaves (DCOQS) The section on the projection formula has been updated with a few results from SGA that I’ve updated to modern standards (i.e. some boundedness hypotheses were removed). This includes the following useful fact: if two perfect complexes are isomorphic on stalks then they are isomorphic on a neighborhood of the point (both isomorphisms are in the respective derived categories).

  I have also included a proof that on a quasi-compact semi-separated scheme every quasi-coherent sheaf can be written as a quotient of a flat quasi-coherent sheaf. This fact is known and is a special case of a published result of Alonso, Jeremias and Lipman.

• Spectral Sequences (SS) I have made a couple of minor corrections and improved the exposition in a few places. Much thanks to Rongmin Lu for pointing out most of these errors.