Timeline for Gossip about Grothendieck and distributive lattices
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
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| Jan 23, 2022 at 14:10 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
added a full citation for the paper
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| Jan 23, 2022 at 13:51 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
fixed the dead link
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| Apr 22, 2020 at 0:07 | history | edited | David Roberts♦ | CC BY-SA 4.0 |
Added a link back
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| Apr 22, 2020 at 0:05 | comment | added | David Roberts♦ | @RobertFurber pdfs.semanticscholar.org/3b4f/… I'll edit it in, together with some minimum identifying information | |
| Apr 21, 2020 at 22:58 | comment | added | Todd Trimble | @RobertFurber I retained the mention of Ernst's thesis, but found some other references which I think will serve just as well. | |
| Apr 21, 2020 at 22:56 | history | edited | Todd Trimble | CC BY-SA 4.0 |
workaround for a broken link
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| Apr 21, 2020 at 22:37 | comment | added | Robert Furber | The link to Ernst's Master's thesis, Multiplicative Ideal Theory, is now broken. It is accessible via a certain site "academia.edu" but it is not open access and requires a log in with Google or Facebook. Does anyone know a legal and morally acceptable link to it? | |
| Apr 21, 2020 at 21:53 | history | made wiki | Post Made Community Wiki by Todd Trimble | ||
| Dec 4, 2010 at 11:07 | comment | added | Todd Trimble | No fair: you and Timothy Chow actually knew Rota! Seriously, that sounds like a good possible explanation, but I keep coming back to this: "Those mathematicians who knew some lattice theory watched with amazement as the algebraic geometers of the Grothendieck school clumsily reinvented the rudiments of lattice theory in their own language." That sounds a lot more like he knows something and is holding back than it does intimations of vague feelings. (By the way, I love the word chutzpah. Did you know that if you play it in a triple-triple line in Scrabble, you can get 383 points?) | |
| Dec 4, 2010 at 2:57 | comment | added | John Baez | I think it's possible to feel sure that if algebraic geometers knew more lattice theory they could do good things, without knowing what these good things would be. I feel things like this all the time. Perhaps it takes a certain chutzpah to put these feeling into print, though. So I'd call Rota's sin "chutzpah" rather than coyness. You're only being coy if you're holding something back. | |
| Oct 10, 2010 at 12:23 | comment | added | Todd Trimble | You're welcome, Pete -- I was puzzled too, not knowing what Rota could have meant by "necessary and sufficient conditions" for CRT, since as you had pointed out, the more familiar version of CRT is a very simple and general thing. So I googled it, and this was one of the results. But I'm still puzzled as to why Rota seems to think that this result is something Grothendieck would have especially benefited from, or whether there's more to the story that he's not telling us. | |
| Oct 10, 2010 at 9:20 | comment | added | Pete L. Clark | Thanks, Todd -- this answers my question very nicely. I am (moderately) familiar with Prufer domains and their characterization via lattice-theoretic properties of their ideals. What I was missing was the precise formulation of CRT as given in the notes you linked to. (I will add though that I have used the "comaximal CRT" many, many times in a variety of contexts, whereas I think I have never needed the Prufer CRT, not even in the special case of Dedekind domains, which I have thought about a fair amount.) | |
| Sep 21, 2010 at 18:51 | comment | added | user6976 | @Todd: Thanks! We still don't have a response from algebraic geometers. Perhaps it is because somebody removed (IMHO unwisely) the alg.geometry tag from the question, or perhaps because there is nothing for them to say. I thought that the connection between lattices and Grothendieck would be related to the etale cohomology and Grothendieck topology which generalized Zariski and Stone topologies. Chinese Remainder Theorem does not need anything outside the ordinary commutative algebra. But perhaps one can apply lattice theory to some generalizations of CRT like the strong approximation? | |
| Sep 20, 2010 at 14:33 | history | answered | Todd Trimble | CC BY-SA 2.5 |