The Rising Sea

Notes Update

November 19, 2005 on 7:22 am | In Note Updates | No Comments

• New Notes: Concentrated Schemes (CON) I’ve added a brief note on quasi-compact quasi-separated schemes (basically just a translation of EGA).

• Modules Over a Scheme (MOS) Has been updated with the more general proof of extension of quasi-coherent sheaves given in EGA, which is then used to prove
  that the category of quasi-coherent sheaves over a concentrated (=quasi-compact quasi-separated) scheme is grothendieck abelian.

• Cohomology of Sheaves (COS) Removed the noetherian hypotheses used in Hartshorne and replaced them with concentratedness, in line with the modern literature. Other related improvements.

• Higher Direct Image of Sheaves (HDIS) Removed noetherian hypotheses of Hartshorne, so that we now show the higher direct image of any concentrated morphism preserves quasi-coherence.