Logarithmic ramifications of étale sheaves by restricting to curves

2017/04/16 by Hu, Haoyu
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1704.04734

Abstract

In this article, we prove that the Swan conductor of an étale sheaf on a smooth variety defined by Abbes and Saito's logarithmic ramification theory can be computed by its classical Swan conductors after restricting it to curves. It extends the same result for rank 1 sheaves due to Barrientos. As an application, we give a logarithmic ramification version of generalizations of Deligne and Laumon's lower semi-continuity property for Swan conductors of étale sheaves on relative curves to higher relative dimensions in a geometric situation.

Related

• Semi-continuity of conductors, and ramification bound of nearby cycles
• Semi-continuity for total dimension divisors of étale sheaves
• Variation of the Swan conductor of an \mathbbF_ℓ-sheaf on a rigid disc
• Semi-continuity for conductor divisors of étale sheaves
• Ramification and nearby cycles for l-adic sheaves on relative curves