Semi-continuity of conductors, and ramification bound of nearby cycles
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Publication:6060808
DOI10.1515/CRELLE-2023-0060arXiv2102.06105OpenAlexW4387300241MaRDI QIDQ6060808
Author name not available (Why is that?)
Publication date: 6 November 2023
Published in: (Search for Journal in Brave)
Abstract: For a constructible 'etale sheaf on a smooth variety of positive characteristic ramified along an effective divisor, the largest slope in Abbes and Saito's ramification theory of the sheaf gives a divisor with rational coefficients called the conductor divisor. In this article, we prove decreasing properties of the conductor divisor after pull-backs. The main ingredient behind is the construction of 'etale sheaves with pure ramifications. As applications, we first prove a lower semi-continuity property for conductors of 'etale sheaves on relative curves in the equal characteristic case, which supplement Deligne and Laumon's lower semi-continuity property of Swan conductors and is also an -adic analogue of Andr'e's semi-continuity result of Poincar'e-Katz ranks for meromorphic connections on complex relative curves. Secondly, we give a ramification bound for the nearby cycle complex of an 'etale sheaf ramified along the special fiber of a regular scheme semi-stable over an equal characteristic henselian trait, which extends a main result in a joint work with Teyssier and answers a conjecture of Leal in a geometric situation.
Full work available at URL: https://arxiv.org/abs/2102.06105
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