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

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

2007-05-19

arxiv.org/abs/0705.2799v2

Journal of the Institute of Mathematics of Jussieu (2009), 8 : 769-829

Mathematics

Algebraic Geometry

56 pages

Scientific paper

10.1017/S1474748008000364

We propose a geometric method to measure the wild ramification of a smooth etale sheaf along the boundary. Using the method, we study the graded quotients of the logarithmic ramification groups of a local field of positive characteristic 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. Definition 2.1.1 is corrected in v2.

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