AI 中文总结
本文为 nowhere 数域 K 构造满足特定性质的 profinite 幺半群 DG_K，研究其与 p-典型 Witt 向量的关系，拓展了绝对伽罗瓦群的形变相关理论。
AI 中文摘要
本文的技术目标是为 nowhere 数域 K 构造并研究 profinite 幺半群 DG_K，满足：1. DG_K 的单位群同构于绝对伽罗瓦群 G_K；2. DG_K 的极大阿贝尔商同构于 Deligne-Ribet 幺半群 DR_K；3. DG_K 的幂等元与 K 的（有限）素数集合 P_K 的子集一一对应；4. 所有带有限分歧 S 的极大伽罗瓦群 G_{K,S} 均作为 DG_K 中幂等元处的极大闭子群出现；5. DG_K 中幂等元处的所有极大闭子群均为此类。我们还讨论了 DG_K 与 Borger 和 de Smit 的 p-典型 Witt 向量之间的关系，特别地，将用局部域 K_p 的范域描述 Borger 和 de Smit 的 Lambda 环半伽罗瓦范畴的基本幺半群。
英文摘要
The technical goal of this paper is to construct and study profinite monoids DG_K for number fields K such that (1) the unit group of DG_K is isomorphic to the absolute Galois group G_K; (2) the maximal abelian quotient of DG_K is isomorphic to the Deligne-Ribet monoid DR_K; (3) the idempotents of DG_K bijectively correspond to subsets of the set P_K of (finite) primes of K; (4) the maximal Galois groups G_{K, S} with restricted ramifications S all appear as maximal closed subgroups of DG_K at idempotents; (5) all maximal closed subgroups of DG_K at idempotents are of this form. We also discuss the relationship between DG_K and the p-typical Witt vectors of Borger and de Smit, where we will describe the fundamental monoid of the semi-galois category of Lambda-rings of Borger and de Smit in terms of fields of norms of the local field K_p in particular.
Commentsdraft; 30 pages. ver3: fixed some typos; gave a better proof (Lemma 3.14); gave a forgotten lemma (Lemma 5.5)
