Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

Characteristic cycle of a rank one sheaf and ramification theory


Author: Yuri Yatagawa
Journal: J. Algebraic Geom. 29 (2020), 471-545
DOI: https://doi.org/10.1090/jag/758
Published electronically: March 9, 2020
MathSciNet review: 4158459
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Abstract | References | Additional Information

Abstract: We compute the characteristic cycle of a rank one sheaf on a smooth surface over a perfect field of positive characteristic. We construct a canonical lifting on the cotangent bundle of Kato’s logarithmic characteristic cycle using ramification theory and prove the equality of the characteristic cycle and the canonical lifting. As corollaries, we obtain a computation of the singular support in terms of ramification theory and the Milnor formula for the canonical lifting.


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Yuri Yatagawa
Affiliation: Department of Mathematics, Saitama University, Saitama, 338-8570, Japan
MR Author ID: 1218497
Email: yatagawa@mail.saitama-u.ac.jp, yatagawa.math@gmail.com

Received by editor(s): January 11, 2018
Received by editor(s) in revised form: August 1, 2019, and November 22, 2019
Published electronically: March 9, 2020
Additional Notes: This work was supported in part by the Program for Leading Graduate Schools, MEXT, Japan, JSPS KAKENHI Grant Number 15J03851, and the CRC 1085 Higher Invariants at the University of Regensburg.
Article copyright: © Copyright 2020 University Press, Inc.