Talk:Beauville–Laszlo theorem

This article uses the "Harvard citations" template, which ought to be deleted. I'm not sure what the best thing is to replace it. See template talk:Harvard citations. Marking for cleanup. Michael Hardy (talk) 22:17, 12 April 2008 (UTC)

I noticed while I was using this template at triangulated category that it has this problem, but there is really no alternative. Searching for "harvard citation" in Templates gives only "Harvard citations" and the similarly-named "Harvard citation", which is insufficient for any sophisticated use. Although the results are ugly, they can (in principle) be fixed in the template. I think it is more likely to produce an effect to lobby at the talk page there, or whatever the forum is for getting changes made to templates, than blaming the articles which use it for being ugly on its account. One could, of course, use footnotes instead of Harvard citations, but I have come to believe that Harvard style is the most readable of the inline citation options; footnotes are very distracting and produce unnecessarily redundant information (link to the footnote, wherein one either writes a Harvard-style reference to the bibliography, or copies an abridged version of the bibliogrpahy entry in question). As a stopgap measure I suppose I could simply replace the inline template with a link to #CITEREFBeauvilleLaszlo1995, but the template must be fixed. Just like we would prefer to use <math></math> instead of HTML markup, so would I prefer to use a template rather than manually formatting my citations. Ryan Reich (talk) 22:40, 12 April 2008 (UTC)

> in the noetherian, finitely-generated case, it is, as noted by the authors, a special case of Grothendieck's faithfully flat descent.

This remark seems to be incorrect. For the faithfully flat descent one also needs the glueing data over the self-intersection ${\hat {A}}\otimes _{A}{\hat {A}}$. In the noetherian case the Beauville-Laszlo theorem reconstructs this missing data. As the authors themselves write in the original French version of their article:

Cependant, comme nous l’ont fait observer V. Drinfeld et M. Rapoport, l’énoncé ne rentre pas directement dans le cadre de la descente fièdlement plate développée par A. Grothendieck. Dans celle-ci, la donnée de descente sur $F\times G$ n’est pas constituée seulement de l’isomorphisme $\phi$, mais aussi d’un isomorphisme ${\hat {A}}\otimes _{A}G\to G\otimes _{A}{\hat {A}}$. — Preceding unsigned comment added by 132.199.67.56 (talk) 14:05, 1 March 2015 (UTC)