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Results tagged with descent
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user 4790
8
votes
Accepted
Are associated bundles representable in schemes?
This is false; there is a counterexample (with $G$ a finite group of order $2$) in my notes on descent theory http://homepage.sns.it/vistoli/descent.pdf, subsection 4.4.2. …
- 27k
8
votes
Accepted
Noetherian descent extension for a given ring
Let $R \to S$ be a descent extension, and assume that $S$ is noetherian. Let $I$ be an ideal of $R$; there will be a finitely generated ideal $J \subseteq I$ of $R$ such that $JS = IS$. …
- 27k
11
votes
Accepted
How does descent theory imply a sheaf is a scheme?
These are covered in my notes on descent theory: the first is in 4.3.1, the second in 4.3.3. … Affine descent applies to the first of the cases you mention, descent via ample line bundles to the second. …
- 27k