Wild ramification, the nearby cycle complexes, and the characteristic cycles of $\ell$-adic sheaves

Abstract

We prove a purely local form of a result of Saito and Yatagawa. They proved that the characteristic cycle of a constructible étale sheaf is determined by wild ramification of the sheaf along the boundary of a compactification. But they had to consider ramification at all the points of the compactification. We give a pointwise result, that is, we prove that the characteristic cycle of a constructible étale sheaf around a point is determined by wild ramification at the point. The key ingredient is to prove that wild ramification of the stalk of the nearby cycle complex of a constructible étale sheaf at a point is determined by wild ramification at the point.

42 pages

References in corpus (4)

• The characteristic cycle and the singular support of a constructible sheaf
• Wild ramification determines the characteristic cycle
• Compatible systems and ramification
• $\ell$-independence of the trace of local monodromy in a relative case

Cited by in corpus (1)

• Cohomological boundedness for flat bundles on surfaces and applications