特征为正的奇点消解：Frobenius-Hasse塔与例外历史下降

中文摘要 AI 辅助

设k为特征p>0的完美域，我们引入k上典范强嵌入消解与主化的对象级构造方案。该构造方案用已处理比较因子的良基历史取代逐点数值不变量的单调性：从标记Rees代数的微分-积分饱和出发，构造全Hasse活动包、滤过系数立方体、半线性Frobenius-Hasse源及普通可允许吹胀的字面变换数据；六行缺陷演算将局部问题导向经认证的曲面、环面单项式、二项式及加法型程序，之后将干净中心序列序列化并在全局 nerve 上下降。核心结构是全局替换证书，其在宏块间传递后继地址、已付商、类型迹、显式父代、重开数据及终端真值；我们证明配备该证书的完备状态可在单个依赖良基序中实现严格多重集替换，故迭代终止且耗尽状态重构出与有序边界具法向交叉的正则严格变换。我们还通过刚性生成、跨代无重置、完全 wild 容量控制、中心或类型退出选项、结构化余纤维、显式父代分配及字面终端真值，表述该证书的对象级实现。该方案页面可在网站 this https URL 获取

英文摘要

Let k be a perfect field of characteristic p>0. We introduce an object-level construction for canonical strong embedded resolution and principalization over k. The construction program replaces monotonicity of pointwise numerical invariants by a well-founded history of addressed comparison factors. Starting from the differential-integral saturation of a marked Rees algebra, we construct total-Hasse activity packets, filtered coefficient cubes, semilinear Frobenius-Hasse sources, and literal transform data for ordinary permissible blowups. A six-row defect calculus routes local problems to certified surface, toroidal-monomial, binomial, and additive-type procedures, after which clean centre portfolios are serialized and descended on a global nerve. The central structure is a global replacement certificate transporting successor addresses, paid quotients, typed traces, displayed parents, reopening data, and terminal truth across macroblocks. We prove that a complete state equipped with this certificate admits a strict multiset replacement in a single dependent well-founded order; hence the iteration terminates and the exhausted state reconstructs a regular strict transform having normal crossings with the ordered boundary. We further formulate an object-level realization of the certificate through rigid generation, cross-generation no-reset, complete wild-capacity control, a centre-or-typed-exit alternative, structured cofibres, displayed-parent allocation, and literal terminal truth. The program page is also available at website https://sites.google.com/view/positive-char-resolution

补充信息

备注

798 pages in nine parts. Program page is available at https://sites.google.com/view/positive-char-resolution Comments are welcome