I have rewritten the introduction to associated points. The new version is available here.
If you are interested in learning about associated points, or solidifying your understanding, or getting a more geometric view of them, please take a look — it is ten pages, and intended to be quite readable to those who have read the first five chapters or so of The Rising Sea.
The new exposition attempts to more directly follow the geometric point of view, set out well for example by Matthew Emerton (perhaps on this blog — if I can find the link I will add it here). I was trying to do something with my previous exposition, but did not succeed, and I think this works better. But I am very interested in hearing what people think, who are reading it right now.
This should be something that you can work through in an evening, and discuss with someone else. I am hoping there will be a couple of epiphanies in there. I am certain there will be typos!
The point of view is summarized here:
(For some reason the letter “p” was deleted in the last line of the pdf above…)
I guess there is no harm in putting the entire thing here, in case someone feels like skimming through it on this page.
Math 216: Foundations of Algebraic Geometry 
July 19, 2022 at 9:52 pm
Thanks for sharing, Ravi. Are you teaching Math 216 online this summer?
Must do lunch soon and catch up. Best, Ashok
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August 9, 2022 at 8:15 pm
I won’t try that online experiment again this summer, but lunch soon sounds good!
July 20, 2022 at 7:07 am
“coherentce”
“The associated points of a module refine the notion of support” I have trouble with singular vs plural here.
“in the rest of this section” is missing a .
“The associated points are precisely the generic points of irreducible components of Supp m for all m ∈ M. The associated points are precisely the generic points of those Supp m which are irreducible.” Is this second sentence missing a word? Definitely I don’t understand it as written, and when I try, I get the first sentence.
“vanishes at no associated point .” has an extra space, like those French weirdos put before question marks.
It’d be nice if you mentioned that the top components of Supp M come with multiplicities. I use these all the time. Then 6.5.B can include the additivity of those multiplicities.
August 9, 2022 at 8:19 pm
Thanks Allen! I’m impressed that you even caught the typo that wasn’t in this precise section. I agree with your suggestions (although I’m disappointed that I didn’t get across the idea in those two sentences (I just gave up and removed the 2nd, and edited the first.
I agree with your “it’d be nice” comment, and indeed I find that important, and likely even use it later. A later tweak (on the drawing board) is to add at an appropriate point a short exercise/minisection on “the Jordan-Holder package”, in which I properly and succinctly include length, and I would want to say this here. (I’m not sure where I get the phrase “package” for a mathematical “package” of ideas —- e.g. “the idempotent package”, or the “smith normal form / f.g. modules over a PID package”. Perhaps indirectly from Dennis Gaitsgory?)
I wish you’d say more about french weirdos. You’re implying that there are some french people who are not weirdos perhaps —what’s an example of a french weirdo, and what’s the example of a french non-weirdo?
August 10, 2022 at 2:42 am
To make clear the phenomenon I’m describing:
“Am I one of those French weirdos?” No.
“Am I one of those French weirdos ?” Yes, assuming you are French.
I believe my phrasing left room for non-French weirdos; I do not see that it implies the existence of French non-weirdos. Incidentally, this word is only two letters’ difference from hairdo.