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ℓ-adic sheaf

Journal of the Institute of Mathematics of Jussieu (1)

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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
Takeshi Saito
Journal:

Journal of the Institute of Mathematics of Jussieu / Volume 8 / Issue 4 / October 2009

Published online by Cambridge University Press:

06 January 2009, pp. 769-829

Print publication:

October 2009
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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.