Logarithmic ramifications of étale sheaves by restricting to curves
Haoyu Hu
Abstract
Open-access reader
Haoyu Hu
Abstract
Open-access reader
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.
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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.
Key concepts: Sheaf, Ramification, Logarithm, Mathematics, Pure mathematics, Rank (graph theory), Conductor, Variety (cybernetics)