Reference for moduli stack of principal G-bundles? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-22T17:02:22Z http://mathoverflow.net/feeds/question/72110 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/72110/reference-for-moduli-stack-of-principal-g-bundles Reference for moduli stack of principal G-bundles? Kevin Lin 2011-08-04T19:08:07Z 2011-08-04T21:05:21Z <p>Hi,</p> <p>I'm looking for a reference for the fact that the moduli stack $M_{GL_r,X}$ of $GL_r$-bundles over $X$ is an algebraic (Artin) stack. I'm only interested in the case where $X$ is a curve (for now).</p> <p>I think this is supposed to be in Laumon-Moret--Bailly's "Champs Algebriques", but my French is not so great and I have been unable to find it in there. If it is actually in there, can you help a non-Francophone out?</p> <p>Thanks!</p> http://mathoverflow.net/questions/72110/reference-for-moduli-stack-of-principal-g-bundles/72112#72112 Answer by Moosbrugger for Reference for moduli stack of principal G-bundles? Moosbrugger 2011-08-04T19:19:12Z 2011-08-04T21:05:21Z <p>I actually don't think$^{\dagger}$ that this example is in Laumon/Moret-Bailey, but Jonathan Wang's senior thesis is a detailed write up in the style of LMB (and in English!) of this fact: <a href="http://math.harvard.edu/theses/senior/wang/wang.pdf" rel="nofollow">http://math.harvard.edu/theses/senior/wang/wang.pdf</a>.</p> <p>$^{\dagger}$ Edit: I stand corrected!</p> http://mathoverflow.net/questions/72110/reference-for-moduli-stack-of-principal-g-bundles/72117#72117 Answer by Jason Starr for Reference for moduli stack of principal G-bundles? Jason Starr 2011-08-04T20:32:57Z 2011-08-04T20:32:57Z <p>This is in LM-B. It is Th&eacute;or&egrave;me 4.6.2.1 on p. 29. A generalization is proved in Max Lieblich's article.</p> <p>MR2233719 (2008c:14022) Lieblich, Max(1-PRIN) Remarks on the stack of coherent algebras. Int. Math. Res. Not. 2006, Art. ID 75273, 12 pp. 14D20 (14A20)</p> <p>Wang's senior thesis is also a well-written source.</p> <p><b>Edit:</b> The reference for Laumon and Moret-Bailly was already posted by Donu. Sorry for missing that.</p>