论文标题
pontryagin二元性，用于紧凑的离散估值环
Pontryagin Duality for Modules over Compact Discrete Valuation Rings
论文作者
论文摘要
我们在紧凑的离散估值环$ r $上建立了pontryagin二元性的类似物。也就是说，我们将拓扑$ r $模块的双重二元定义为其连续的$ r $ module同构为$ k/r $，$ k/r $是其整数圈的分数字段的商模块。可以确定的是，对于本地紧凑的$ r $模型，双重二映射是同构和同构。此外，鉴于非题为$ r $ $模块的构造，构造了一个规范的拓扑，并唯一定义，以使双重二级映射将具有凹入性和连续性。最后，将模块分配给配备典型拓扑的模块的函子被证明是完全忠实的，从而使人们可以以纯粹的代数形式重新定义拓扑陈述。
We establish an analogue of Pontryagin duality for modules over compact discrete valuation rings $R$. Namely, we define the dual of a topological $R$ module to be its continuous $R$-module homomorphisms into $K/R$, the quotient module of the fraction field by its ring of integers. It is established that for locally compact $R$-modules the double dual map is an isomorphism and homeomorphism. Additionally, given a non-topological $R$-module a canonical topology is constructed, uniquely defined so that the double dual map will be injective and continuous. Finally, the functor assigning a module to itself equipped with canonical topology is shown to be fully faithful, allowing one to recontextualize the topological statements in purely algebraic forms.
