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I am reading Joseph Bernstein's notes on D-modules which are available online here

In section 1 (page 1 of the pdf) Bernstein writes "By Serre's theorem this condition is local."

I was wondering to what theorem Bernstein is referring and wondering where I could find a statement and proof of this theorem.

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    @Gunnar Magnusson - Nice! I thought I had heard this joke before. My friends and I have a running joke where if you forget the author of theorem it becomes attributed to either Euler or Gauss.2010-12-07

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I believe the first theorem in article 1.2 here

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    This looks like exactly what I needed, thanks!2010-12-07