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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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    "By Serre's Theorem..." My sympathies: there are many results to choose from!2010-12-07
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    @Pete L. Clark at least it wasn't "by a theorem of Euler" :)2010-12-07
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    Have you seen Serre's talk on how to write mathematics badly? He has this comment about how the phrase "a theorem of Euler" carries no information, this seems kind of related. ;) (Incidentally, me and a friend defined the Serre numbers $S_k$ of a talk once while bored. $S_0$ is the number of times Serre made comments during the talk (usually zero). $S_1$ is the number of results of Serre referenced by the speaker, $S_2$ the number of results used which depend on a result by Serre, etc. The conjecture is that the Serre numbers of any talk on algebraic geometry are all finite.)2010-12-07
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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