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Wild ramification and the characteristic cycle of an ℓ-adic sheaf

Part of: Algebraic number theory: local and $p$-adic fields (Co)homology theory

Published online by Cambridge University Press:  06 January 2009

Takeshi Saito
Takeshi Saito
Affiliation:
Department of Mathematical Sciences, University of Tokyo, Tokyo 153-8914, Japan (t-saito@ms.u-tokyo.ac.jp)
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Abstract

We propose a geometric method to measure the wild ramification of a smooth étale sheaf along the boundary. Using the method, we study the graded quotients of the logarithmic ramification groups of a local field of characteristic p > 0 with arbitrary residue field. We also define the characteristic cycle of an ℓ-adic sheaf, satisfying certain conditions, as a cycle on the logarithmic cotangent bundle and prove that the intersection with the 0-section computes the characteristic class, and hence the Euler number.

Keywords

ℓ-adic sheafwild ramificationcharacteristic cycle

MSC classification

Secondary: 14F20: Étale and other Grothendieck topologies and (co)homologies 11S15: Ramification and extension theory
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 8 , Issue 4 , October 2009 , pp. 769 - 829
Copyright
Copyright © Cambridge University Press 2008

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