Timeline for a question about Beauville-Laszlo
Current License: CC BY-SA 3.0
3 events
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| Feb 25, 2013 at 12:30 | comment | added | user28172 | In the noetherian case, BL is a special case of usual faithfully flat descent. For any noetherian ring $R$ (such as $V[[u,v]]/(uv-\pi)$) and any $\pi \in R$, an element of $R$ divisible by $\pi$ in the $\pi$-adic completion $R'$ of $R$ is divisible by $\pi$ in $R$ because the natural map $R/\pi R \rightarrow R'/\pi R'$ is injective (even an isomorphism), and the diagonal map $R \rightarrow R[1/\pi] \times R'$ is injective (by faithful flatness considerations locally along the zeros of $\pi$ in Spec($R$)), so the $F$ you ask about is always the original noetherian ring $R$. | |
| Feb 25, 2013 at 11:00 | history | edited | questio | CC BY-SA 3.0 |
added 64 characters in body
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| Feb 25, 2013 at 9:05 | history | asked | questio | CC BY-SA 3.0 |