AI 中文总结
该研究分析二维p有界晶态轨迹Z(r)的包含关系，除退化情形外通过三种Hodge型运算分类，除一例外可通过闭点包含检测，研究中大量使用GPT-5.5 Pro。
AI 中文摘要
设p为奇素数，K/Qₚ是次数f>1的有限非分歧扩张。令Z(r)为K的绝对伽罗瓦群的二维晶态表示的Hodge型r的Emerton-Gee栈的约化特殊纤维。我们研究当r取遍p有界Hodge型时，栈Z(r)的集合在包含关系下的偏序集合。我们证明，除两种退化情形外，简单包含关系可通过Hodge型的三种运算分类，其中两种具有标准自守解释。我们还证明，除一种例外，包含关系可通过闭点的包含关系（等价于半单模p伽罗瓦表示）检测。本工作过程中大量使用了GPT-5.5 Pro。
英文摘要
Let p be an odd prime and K/Qp a finite unramified extension of degree f > 1. Let Z(r) be the reduced special fiber of the Emerton-Gee stack of two-dimensional crystalline representations of Hodge type r of the absolute Galois group of K. We study the collection of stacks Z(r) as r varies over p-bounded Hodge types, as a set partially ordered under inclusion. We prove that aside from two degenerate cases, simple inclusions can be classified in terms of three operations on Hodge types, two of which have standard automorphic interpretations. We also prove, with one exception, that inclusions can be detected at the level of an inclusion of closed points (equivalently, semisimple mod p Galois representations). GPT-5.5 Pro was used extensively in the course of this work.
Comments31 pages
