A symplectic look at the Fargues-Fontaine curve
A symplectic look at the Fargues-Fontaine curve
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法格-方丹曲线的辛观察
DOI：
10.1017/fms.2021.83
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Lekili Y
中科院分区：
文献类型：
--
作者：
Lekili Y
我们研究辛 2-环面的 Fukaya 范畴的一个版本，其系数位于局部恒定的环束中。环束包括全局定义的诺维科夫参数，该参数在按区域组织多边形计数方面发挥其通常的作用。它还包括一个常数环，其围绕环面的变化可以通过一对交换环自同构来编码。当这些常数是特征 p 的完美类时，其中一个完整函数是微不足道的，另一个是幂映射，则可以以有限的方式将诺维科夫参数特化为 1。我们证明了定义的 Dehn 扭转环与 Fargues 和 Fontaine 引入的齐次坐标环同构：他们的局部场 的“p-adic Hodge 理论曲线”。
We study a version of the Fukaya category of a symplectic 2-torus with coefficients in a locally constant sheaf of rings. The sheaf of rings includes a globally defined Novikov parameter that plays its usual role in organising polygon counts by area. It also includes a ring of constants whose variation around the the torus can be encoded by a pair of commuting ring automorphisms. When these constants are perfectoid of characteristic p, one of the holonomies is trivial and the other is the power map, it is possible in a limited way to specialise the Novikov parameter to 1. We prove that the Dehn twist ring defined there is isomorphic to the homogeneous coordinate ring of a scheme introduced by Fargues and Fontaine: their ‘curve of p-adic Hodge theory’ for the local field .