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

Publisher： Cambridge University Press

E-ISSN： 1475-3030|8|4|769-829

ISSN： 1474-7480

Source： Journal of the Institute of Mathematics of Jussieu, Vol.8, Iss.4, 2009-10, pp. : 769-829

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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.

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