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

Abstract

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.

56 pages

References in corpus (3)

• Structure des connexions méromorphes formelles de plusieurs variables et semi-continuité de l'irrégularité
• The characteristic class and ramification of an l-adic etale sheaf
• A correction to Epp's paper "Elimination of wild ramification"

Cited by in corpus (14)

• Ramification of local fields with imperfect residue fields III
• Wild Ramification and the Cotangent Bundle
• Coincidence of two Swan conductors of abelian characters
• On ramification filtrations and $p$-adic differential modules, I: equal characteristic case
• On localizations of characteristic classes of l-adic sheaves of rank 1
• Ramification groups of coverings and valuations
• Introductory course on $\ell$-adic sheaves and their ramification theory on curves
• Parallel transport for vector bundles on p-adic varieties
• Ramification and cleanliness
• Ramification and nearby cycles for l-adic sheaves on relative curves
• On the ramification of non-abelian Galois coverings of degree $p^3$
• Cleanliness and log-characteristic cycles for vector bundles with flat connections
• Characteristic cycle of a rank one sheaf and ramification theory
• Variation of the Swan conductor of an ${\mathbb{F}}_{\ell }$-sheaf on a rigid disc