Logarithmic ramifications of étale sheaves by restricting to curves

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.

arXiv comment26 pages. Comments are welcome

References in corpus (2)

• Structure des connexions méromorphes formelles de plusieurs variables et semi-continuité de l'irrégularité
• Relative singular support and the semi-continuity of characteristic cycles for étale sheaves