Timeline for Primes that must occur in every composition series for a given module
Current License: CC BY-SA 2.5
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 9, 2010 at 18:53 | vote | accept | Steven Landsburg | ||
| Dec 8, 2010 at 14:19 | comment | added | Steven Landsburg | Hailong: For the application I had in mind, I'd want to consider distinct prime ideals as different, even if they are the same as modules. | |
| Dec 8, 2010 at 3:17 | comment | added | Hailong Dao | Hi Steven, a silly question: if $P\cong Q$ as $R$-modules, do you consider them the same? I asked because for example if $R$ is a domain, then $(f) \cong (g)$ for any 2 elements $f,g$ but $R/(f)$ and $R/(g)$ are not isomorphic unless f=g*unit. | |
| Dec 7, 2010 at 7:08 | answer | added | Hailong Dao | timeline score: 10 | |
| Dec 7, 2010 at 6:57 | comment | added | Hailong Dao | I see, in fact I have a K-theoretic answer in mind! I will post it, but may be you can ask your original question, it looks very interesting! | |
| Dec 7, 2010 at 6:37 | comment | added | Steven Landsburg | Hailong: The problem is interesting even in the smooth case; for understanding K-theory relative to a collection of subschemes, for example, where the "well behaved subcategory" should consist of modules that meet all those subschemes in higher codimensions. | |
| Dec 7, 2010 at 6:33 | comment | added | Steven Landsburg | Hailong: Given two modules with the same support, one would ideally like to believe that they represent the same class in $K$-theory up to classes of modules from some well-behaved subcategory. (This is true in the smooth case, with the well-behaved subcategory being modules of higher codimension --- but in the singular case one often wants a more restricted subcategory, e.g. modules that not only have higher codimension but also meet the singular locus in higher codimension.) Primes in ${\cal C}(M)$ are potential obstructions to that program, so one wants to understand those primes. | |
| Dec 7, 2010 at 6:06 | comment | added | Hailong Dao | Hi Steven, nice question! I am just curious, could you share the motivation with us? | |
| Dec 7, 2010 at 5:34 | history | asked | Steven Landsburg | CC BY-SA 2.5 |