finite etale covering of stacks - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-20T19:45:35Z http://mathoverflow.net/feeds/question/21637 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/21637/finite-etale-covering-of-stacks finite etale covering of stacks shenghao 2010-04-17T01:29:35Z 2010-04-17T01:29:35Z <p>If $Y \to X$ is a finite etale map of schemes, then there exists a finite Galois morphism $Z \to X$ (i.e. it's a $Aut(Z/X)$-torsor) that factors as $Z \to Y \to X.$ The case when $X$ is normal is easy to prove: take the galois closure of function field of $Y$ and then take the normalization of $X$ in it. The general case is proved in Murre's book. </p> <p>My question is, is this true for stacks? Namely if $Y \to X$ is a representable finite etale map of algebraic stacks, can it be refined to a representable Galois morphism $Z \to X?$ </p>