Stiefel-Whitney classes of curve covers

Björn Selander Tomtebogatan 18, Stockholm, Sweden

Algebraic Geometry K-Theory and Homology mathscidoc:1701.01012

Arkiv for Matematik, 1-18, 2013.10
Let $D$ be a Dedekind scheme with the characteristic of all residue fields not equal to 2. To every tame cover $C\to D$ with only odd ramification we associate a second Stiefel-Whitney class in the second cohomology with mod 2 coefficients of a certain tame orbicurve $[D]$ associated to $D$ . This class is then related to the pull-back of the second Stiefel-Whitney class of the push-forward of the line bundle of half of the ramification divisor. This shows (indirectly) that our Stiefel-Whitney class is the pull-back of a sum of cohomology classes considered by Esnault, Kahn and Viehweg in ‘Coverings with odd ramification and Stiefel-Whitney classes’. Perhaps more importantly, in the case of a proper and smooth curve over an algebraically closed field, our Stiefel-Whitney class is shown to be the pull-back of an invariant considered by Serre in ‘Revêtements à ramification impaire et thêta-caractéristiques’, and in this case our arguments give a new proof of the main result of that article.
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  title={Stiefel-Whitney classes of curve covers},
  author={Björn Selander},
  booktitle={Arkiv for Matematik},
Björn Selander. Stiefel-Whitney classes of curve covers. 2013. In Arkiv for Matematik. pp.1-18.
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