Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 

 

Wild ramification and the cotangent bundle


Author: Takeshi Saito
Journal: J. Algebraic Geom. 26 (2017), 399-473
DOI: https://doi.org/10.1090/jag/681
Published electronically: September 19, 2016
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Abstract | References | Additional Information

Abstract: We define the characteristic cycle of a locally constant étale sheaf on a smooth variety in positive characteristic ramified along the boundary as a cycle in the cotangent bundle of the variety, at least on a neighborhood of the generic point of the divisor on the boundary. The crucial ingredient in the definition is the commutative group structure on the boundary induced by the groupoid structure of multiple self-products.

We prove a compatibility with pull-back and local acyclicity in non-characteristic situations. We also give a relation with the cohomological characteristic class under a certain condition and a concrete example where the intersection with the 0-section computes the Euler-Poincaré characteristic.


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Additional Information

Takeshi Saito
Affiliation: School of Mathematical Sciences, University of Tokyo, Tokyo 153-8914, Japan
Email: t-saito@ms.u-tokyo.ac.jp

DOI: https://doi.org/10.1090/jag/681
Received by editor(s): April 10, 2014
Received by editor(s) in revised form: July 24, 2015, and August 26, 2015
Published electronically: September 19, 2016
Article copyright: © Copyright 2016 University Press, Inc.

Journal of Algebraic Geometry
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