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A British mathematician was giving a talk in Grothendieck’s seminar in Paris. He started “Let X be a variety…”. This caused some talking among the students sitting in the back, who were asking each other “What’s a variety?”. J.-P. Serre, sitting in the front row, turns around a bit annoyed and says “Integral scheme of finite type over a field”.
I don’t get it.
The way I interpret the joke is that Serre’s answer to the student’s won’t really help them; they didn’t know what “variety” meant in this context and the definition they were given by Serre is extremely abstract. I’m guessing there is an extra “hidden” punchline for those familiar with Serres work (which I’m not, unfortunately).
So what youre saying is that you don’t know either…