Semi-continuity of conductors, and ramification bound of nearby cycles
Semi-continuity of conductors, and ramification bound of nearby cycles
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DOI：
10.1515/crelle-2023-0060
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发表时间：
2021-02
期刊：
影响因子：
--
通讯作者：
Haoyu Hu
中科院分区：
文献类型：
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作者：
Haoyu Hu
摘要 对于沿有效除数分支的正特性光滑簇上的可构造 etale 束，Abbes 和 Saito 的束分支理论中的最大斜率给出了一个具有有理系数的除数，称为导体除数。在本文中，我们证明了回拉后导体除数的递减特性。其背后的主要成分是具有纯粹分支的 étale 滑轮结构。作为应用，我们首先证明了相同特征情况下相对曲线上 étale 滑轮导体的下半连续性，它补充了 Deligne 和 Laumon 的 Swan 导体的下半连续性（[33]），也是 André 的复杂相对曲线上亚纯连接的 Poincaré-Katz 等级半连续结果的 ℓ {\ell} -adic 类似物。 （[6]）。其次，我们给出了一个 étale 束的邻近循环复合体的分枝界，该复合体沿着规则方案半稳定的特殊纤维在相等的特征亨塞尔特征上分枝，这扩展了与 Teyssier ([20]) 联合工作的主要结果，并在几何情况下回答了 Leal ([35]) 的猜想。
Abstract For a constructible étale 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 étale sheaves with pure ramifications. As applications, we first prove a lower semi-continuity property for conductors of étale sheaves on relative curves in the equal characteristic case, which supplement Deligne and Laumon’s lower semi-continuity property of Swan conductors ([33]) and is also an ℓ {\ell} -adic analogue of André’s semi-continuity result of Poincaré–Katz ranks for meromorphic connections on complex relative curves. ([6]). Secondly, we give a ramification bound for the nearby cycle complex of an étale 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 ([20]) and answers a conjecture of Leal ([35]) in a geometric situation.