混合特征中的测试理想：一个直到扰动的统一理论
代数几何
2025-07-10 v2 交换代数
摘要
设X是混合特征完备DVR上的有限型整概形。我们给出了测试理想的定义，该定义在p可逆后与乘子理想一致，由足够大的变更计算，在任意剩余特征为p的点处完备化后与之前的混合特征BCM测试理想一致（直到小扰动），并且满足乘子理想或测试理想的全部预期性质。该对象通过p进Riemann-Hilbert函子得到。
引用
@article{arxiv.2401.00615,
title = {Test ideals in mixed characteristic: a unified theory up to perturbation},
author = {Bhargav Bhatt and Linquan Ma and Zsolt Patakfalvi and Karl Schwede and Kevin Tucker and Joe Waldron and Jakub Witaszek and Rankeya Datta},
journal= {arXiv preprint arXiv:2401.00615},
year = {2025}
}
备注
117 pages, major revision, improved results (removed completeness hypothesis from base DVR, better perturbation/test elements), added appendix by Rankeya Datta, other minor changes and typos corrected, comments welcome