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I've recently been reading about Euler systems, and was curious where the name comes from. In particular, while the notion of an Euler system is still not rigorously defined, does the idea resemble something of Euler's, or is the name purely coincidental?

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I'm pretty sure it comes from "Euler factors." –  Cam McLeman Feb 17 '13 at 1:18
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en.wikipedia.org/wiki/Euler_system explains the origin. –  Misha Feb 17 '13 at 5:59
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What makes you say that the idea of an Euler system is not rigorously defined? See e.g. chapter 2 of Rubin's book "Euler systems". –  David Loeffler Feb 17 '13 at 11:57
    
I have looked through Rubin's book, and there does exist an attempt at a definition. However, it does not capture the anti-cyclotomic Euler system that Kolyvagin defined (yes, Rubin does include that later too...). But there are so few examples of Euler systems, that it seems unlikely Rubin's captures precisely the properties to describe such a phenomenon. –  Lucy Feb 17 '13 at 17:44
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You could also have a look at the introduction of Kato's article in Astérisque 295 for a nice overview of the ideas behind introducing Euler systems. –  François Brunault Feb 18 '13 at 13:42
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