Timeline for Reflexive vs. pseudo-coherent abelian groups
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Feb 9, 2021 at 13:10 | history | edited | Jakob | CC BY-SA 4.0 |
rephrase the question
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| Feb 9, 2021 at 13:09 | comment | added | Jakob | @Yai0Phah: Thanks - I think you are right, the assertion I made in the question is unclear. It might still be correct if R has finite global dimension. I will edit the question accordingly. | |
| Feb 8, 2021 at 11:59 | comment | added | user20948 | @R.vanDobbendeBruyn I found that this is false even when $i=1$. | |
| Feb 8, 2021 at 11:34 | comment | added | user20948 | @R.vanDobbendeBruyn Is it obvious that all higher Ext groups $\operatorname{Ext}^i(\prod_{\mathbb N}\mathbb Z,\mathbb Z)$ vanish? The OP mentioned that the reflexivity in question is derived. | |
| Feb 8, 2021 at 11:28 | comment | added | user20948 | Sorry for my ignorance: why are pseudocoherent modules "derived" reflexive? For example, I don't know whether $\operatorname{Hom}_R(K_*,R)$ is K-projective when $K_*$ is a homologically bounded below complex of free modules. Note that the dual is not ncessarily bounded below. | |
| May 15, 2020 at 15:53 | comment | added | R. van Dobben de Bruyn | Small comment: if $R$ is Noetherian, then pseudo-coherent just means finitely generated. In the non-derived sense, reflexive does not imply finitely generated; for example $\mathbf Z^{(\mathbf N)}$ is reflexive. This depends highly on the ring; for example for a DVR $R$ the analogous result is true if and only if $R$ is not complete; see e.g. this post. | |
| May 15, 2020 at 13:24 | history | edited | Jakob | CC BY-SA 4.0 |
integers
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| May 15, 2020 at 12:51 | history | asked | Jakob | CC BY-SA 4.0 |