Logarithmic growth filtrations for ( φ , ∇ )-modules over the bounded Robba ring
Logarithmic growth filtrations for ( φ , ∇ )-modules over the bounded Robba ring
复制标题
有界 Robba 环上 ( φ , ∇ ) 模的对数增长过滤
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发表时间：
2018
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通讯作者：
Shun Ohkubo
中科院分区：
文献类型：
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作者：
Shun Ohkubo
在本文中，我们研究了对数增长（log-growth）过滤，这是 B. Dwork 发现的一个神秘的不变量，适用于有界 Robba 环上的 (φ,∇) 模。主要结果证明了 B. Chiarelloto 和 N. Tsuzuki 提出的关于对数增长过滤和 Frobenius 斜率过滤比较的猜想。证明的要素之一是纯有界商的新标准，这是 Chiarelloto 和 Tsuzuki 为阐述他们的猜想而引入的概念。我们还给出了对数增长牛顿多边形的几个应用，包括 Dwork 对半连续性的猜想，以及 V. Drinfeld 和 K. Kedlaya 在不可分解收敛 F 等晶体的 Frobenius 牛顿多边形上的定理的模拟。
In this paper, we study the logarithmic growth (log-growth) filtration, a mysterious invariant found by B. Dwork, for (φ,∇)-modules over the bounded Robba ring. The main result is a proof of a conjecture proposed by B. Chiarellotto and N. Tsuzuki on a comparison between the log-growth filtration and Frobenius slope filtration. One of the ingredients of the proof is a new criterion for pure of bounded quotient, which is a notion introduced by Chiarellotto and Tsuzuki to formulate their conjecture. We also give several applications to log-growth Newton polygons, including a conjecture of Dwork on the semicontinuity, and an analogue of a theorem due to V. Drinfeld and K. Kedlaya on Frobenius Newton polygons for indecomposable convergent F -isocrystals.