Timeline for Unibranch partial normalization
Current License: CC BY-SA 3.0
3 events
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| Aug 31, 2015 at 14:32 | comment | added | grghxy | The key thing about curves (over a field, say) is that the normalization $\widetilde{R}$ of a local ring $R$ at a closed point is not only module-finite but the cokernel $R$-module $\widetilde{R}/R$ is of finite length (as curves have dimension 1) and so is unaffected by scalar extension to the henselization $R^{\rm{h}}$. That is why one can "pull down" irreducible components of the normalization of $R^{\rm{h}}$ to get an $R$-subalgebra of $\widetilde{R}$ to define a "unbranched partial normalization". It seems unrealistic to expect anything like that beyond dimension 1. | |
| Aug 31, 2015 at 9:38 | history | edited | Piotr Achinger | CC BY-SA 3.0 |
changed link to point to arxiv abstract page rather than directly to pdf
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| Aug 31, 2015 at 8:46 | history | asked | user78294 | CC BY-SA 3.0 |