Timeline for Why Cohen-Macaulay rings have become important in commutative algebra?
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Oct 9, 2013 at 5:57 | answer | added | Gil Kalai | timeline score: 5 | |
| Aug 9, 2013 at 16:47 | vote | accept | user66733 | ||
| Jul 31, 2013 at 20:16 | answer | added | Darius Math | timeline score: 4 | |
| Jul 31, 2013 at 4:04 | answer | added | Karl Schwede | timeline score: 33 | |
| Jul 31, 2013 at 1:40 | answer | added | Vidit Nanda | timeline score: 11 | |
| Jul 31, 2013 at 0:57 | history | migrated | from math.stackexchange.com (revisions) | ||
| Jul 30, 2013 at 21:22 | comment | added | Makoto Kato | Wikipedia: They are named for Francis Sowerby Macaulay (1916), who proved the unmixedness theorem for polynomial rings, and for Cohen (1946), who proved the unmixedness theorem for formal power series rings. All Cohen–Macaulay rings have the unmixedness property. | |
| Jul 30, 2013 at 18:32 | comment | added | Makoto Kato | Serre's FAC refers to theorem of Cohen-Macaulay in Samuel's Alegre Locale(1953). It states that a system of parameters of a regular local ring is a regular sequence. Zariski-Samuel's book(1958) defines Cohen-Macaulay local ring(they call it Macaulay ring). | |
| Jul 30, 2013 at 17:04 | comment | added | Sam Hopkins | You said you're studying Stanley-Reisner rings, so I assume you've read this, but this seminal paper does immediately demonstrate the relevance of Cohen-Macaulay rings to combinatorial commutative algebra: dedekind.mit.edu/~rstan/pubs/pubfiles/27.pdf | |
| Jul 30, 2013 at 14:01 | comment | added | Matt | I don't know about historically, but one major reason in modern days is geometry. It turns out that if you form a "good" moduli space (insert some stability notion) of smooth varieties of some type, then they degenerate at the boundary to some singular varieties. It turns out that these will have at worst Cohen-Macaulay singularities, so understanding Cohen-Macaulay rings is extremely important in the study of classifying smooth varieties. | |
| Jul 30, 2013 at 9:27 | history | asked | user66733 | CC BY-SA 3.0 |