Timeline for Question on bigraded modules
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
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| Oct 15, 2012 at 22:00 | answer | added | Ralph | timeline score: 1 | |
| Oct 15, 2012 at 15:13 | history | edited | Knot | CC BY-SA 3.0 |
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| Oct 15, 2012 at 14:53 | comment | added | Pablo Zadunaisky | $M^{(n)}$ is not stable by multiplication by $T_j$, since this increases the "$n$", so it only has the structure of an $R$-module. On the other hand, this assignation must be exact because a complex of $S$-modules is exact if and only if it is exact when we look at each component separately. | |
| Oct 15, 2012 at 13:58 | comment | added | Knot | @Ralph: You are right. In fact, I proved it but I am not sure about it, the graded structure confuses me. | |
| Oct 15, 2012 at 13:51 | comment | added | Ralph | It seems to me that your functor is from the category of bigraded S-modules to the category of graded R-modules, but I didn't check details yet. | |
| Oct 15, 2012 at 13:40 | comment | added | Knot | @Ralph: Thank you, I have confused with $R$ and $S$. The 2nd question is in fact a results of a lemma in a paper, that I do not think it is trivial but I have not proved it yet, so I decided to post it here. Thank you very much! P.s : The functor is from the category of bigraded modules to the category of bigraded module, I think. | |
| Oct 15, 2012 at 13:38 | history | edited | Knot | CC BY-SA 3.0 |
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| Oct 15, 2012 at 13:29 | comment | added | Ralph | (1) Shouldn't M be a bigraded S-module ? (2) What are the categories mapped by your functor ? (3) Which kind of isomorphism do you expect in the 2nd question ? | |
| Oct 15, 2012 at 4:19 | history | edited | Knot | CC BY-SA 3.0 |
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| Oct 15, 2012 at 3:56 | comment | added | Knot | @Mariano Suarez-Alvarez : Thank you very much! I edited it. | |
| Oct 15, 2012 at 3:55 | history | edited | Knot | CC BY-SA 3.0 |
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| Oct 15, 2012 at 3:32 | comment | added | Mariano Suárez-Álvarez | You introduced the polynomials $f_i$ and the ring $S$ in your first paragraph, but did not use it there. Is there a type somewhere? | |
| Oct 15, 2012 at 3:16 | history | asked | Knot | CC BY-SA 3.0 |