Regular singular stratified bundles and tame ramification
Abstract
Let X be a smooth variety over an algebraically closed field k of positive characteristic. We define and study a general notion of regular singularities for stratified bundles (i.e. O_Xcoherent D_Xmodules) on X without relying on resolution of singularities. The main result is that the category of regular singular stratified bundles with finite monodromy is equivalent to the category of continuous representations of the tame fundamental group on finite dimensional kvector spaces. As a corollary we obtain that a stratified bundle with finite monodromy is regular singular if and only if it is regular singular along all curves mapping to X.
 Publication:

arXiv eprints
 Pub Date:
 October 2012
 DOI:
 10.48550/arXiv.1210.5077
 arXiv:
 arXiv:1210.5077
 Bibcode:
 2012arXiv1210.5077K
 Keywords:

 Mathematics  Algebraic Geometry;
 14E20;
 14E22
 EPrint:
 26 pages, to appear in Trans. Amer. Math. Soc., minor changes