Hodge–Tate 棱柱晶体与 Sen 理论
数论
2023-11-28 v2 代数几何
摘要
我们研究 O_K 的绝对（对数-）棱柱位点上的 Hodge–Tate 晶体，其中 O_K 是具完美剩余域的混合特征完备离散赋值环。我们首先通过配备某些小自同态的 O_K-模对 Hodge–Tate 晶体进行分类。随后我们在非伽罗瓦 Kummer 塔上构造 Sen 理论，并用它将有理 Hodge–Tate 晶体分类为（对数-）近 Hodge–Tate 表示。在此过程中证明了多种上同调比较与消没结果。
引用
@article{arxiv.2311.07024,
title = {Hodge--Tate prismatic crystals and Sen theory},
author = {Hui Gao and Yu Min and Yupeng Wang},
journal= {arXiv preprint arXiv:2311.07024},
year = {2023}
}
备注
v1:This preprint contains almost all results of arXiv:2112.10140 (except section 5 there) and all results of arXiv:2201.10136 . Furthermore, all results are generalized to the log-prismatic setting. Incidentally, this preprint has a same title as arxiv:2201.10136; we apologize for possible confusions. v2: improved exposition, very minor revisions. Comments are welcome