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Transactions of the American Mathematical Society

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Regular singular stratified bundles and tame ramification


Author: Lars Kindler
Journal: Trans. Amer. Math. Soc. 367 (2015), 6461-6485
MSC (2010): Primary 14E20, 14E22
DOI: https://doi.org/10.1090/S0002-9947-2014-06143-6
Published electronically: November 13, 2014
MathSciNet review: 3356944
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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.  $ \mathcal {O}_X$-coherent $ \mathscr {D}_{X/k}$-modules) 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 $ k$-vector 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$.


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Lars Kindler
Affiliation: Mathematisches Institut, Freie Universität Berlin, Arnimallee 3 Room 112A, 14195 Berlin, Germany

DOI: https://doi.org/10.1090/S0002-9947-2014-06143-6
Received by editor(s): October 18, 2012
Received by editor(s) in revised form: August 5, 2013
Published electronically: November 13, 2014
Additional Notes: This work was supported by the Sonderforschungsbereich/Transregio 45 “Periods, moduli spaces and the arithmetic of algebraic varieties” of the DFG
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.