A universal étale lift of a proper local embedding

Details A universal étale lift of a proper local embedding A universal étale lift of a proper local embedding

2010-11-06

arxiv.org/abs/1011.1596v1

Mathematics

Algebraic Geometry

Scientific paper

To any finite local embedding of Deligne--Mumford stacks $g: Y\to X$ we associate an \'etale, universally closed morphism $F_{Y/X}\to X$ such that for the complement $Y^2_X$ of the image of the diagonal $Y \to Y\times_XY$, the stack $F_{Y^2_X/Y}$ admits a canonical closed embedding in $F_{Y/X}$, and $F_{Y/X}\times_XY$ is a disjoint union of copies of $F_{Y^2_X/Y}$. The stack $F_{Y/X}$ has a natural functorial presentation, and the morphism $F_{Y/X}\to X$ commutes with base-change. The image of $Y^2_X$ in $Y$ is the locus of points where the morphism $Y \to g(Y)$ is not smooth. Thus for many practical purposes, the morphism $g$ can be replaced in a canonical way by copies of the closed embedding $F_{Y^2_X/Y}\to F_{Y/X}$.

Affiliated with

Also associated with

No associations

Rating

A universal étale lift of a proper local embedding does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A universal étale lift of a proper local embedding, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A universal étale lift of a proper local embedding will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-245741