Weyl代数的热带化与多面体完备化
Tropicalization and Polyhedral Completions of Weyl Algebras
AI总结：
该研究在完备非阿基米德域上构造Weyl代数的多面体完备化，证明离散赋值域上Γ-有理完备化的双侧平坦性，构造紧整多面体的整模型并描述其特殊纤维与高斯点约化。
摘要：
我们在完备非阿基米德域上构造Weyl代数的加权与多面体完备化，并将其组织为多面体G- site上的结构层。对于离散赋值域，我们证明Γ-有理多面体完备化的双侧平坦性，由此得到有限生成D-模的正基变换；对于紧整多面体，我们还构造有限型整模型，其特殊纤维为环面面环，并通过环面层描述高斯点的约化。
英文摘要：
We construct weighted and polyhedral completions of the Weyl algebra over a complete nonarchimedean field and organize them into a structure sheaf on a polyhedral $G$-site. For discretely valued fields, we prove two-sided flatness for $Γ$-rational polyhedral completions, yielding exact base change for finitely generated $D$-modules. For compact integral polyhedra, we also construct finite-type integral models whose special fibers are toric face rings and describe the reduction of Gauss points in terms of toric strata.
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