一致刚性空间与形式有限型Néron模型
Uniformly rigid spaces and Néron models of formally finite type
摘要：
在完备离散域上引入一类新的非阿基米德解析空间。这些空间，我们称之为一致刚性的，可以看作是经典的刚性解析空间，加上一个额外的一致结构：在点的水平上，一致刚性空间与它的底层刚性空间重合，而它的G-拓扑更粗糙，它的全纯函数层更小。一个均匀刚性结构，局部，诱导的形式有限型的整体形式模型。事实上，贝特洛的一般纤维函子因子自然地通过一致刚性空间的范畴。形式有限型的拟紧形式概形的一致刚性泛纤维是拟紧的，且其整体函数是有界的。我们从半仿射代数和嵌套的有理覆盖出发，构建我们的新类别，我们证明了一个一致刚性无环性定理，我们研究相干模块。然后我们定义一致刚性空间的形式Néron模型为满足泛Néron性质的形式有限型的光滑形式概形。我们建立了某些类一致刚性群的形式Néron模型的存在性，并讨论了Chai程序在计算具有潜在乘性约化的阿贝尔簇的基变导体方面的应用。这篇论文是作者博士论文的忠实副本。
英文摘要：
We introduce a new category of non-archimedean analytic spaces over a complete discretely valued field. These spaces, which we call uniformly rigid, may be viewed as classical rigid-analytic spaces together with an additional uniform structure: On the level of points, a uniformly rigid space coincides with its underlying rigid space, while its G-topology is coarser and its sheaf of holomorphic functions is smaller. A uniformly rigid structure is, locally, induced by an integral formal model of formally finite type. In fact, Berthelot's generic fiber functor factors naturally through the category of uniformly rigid spaces. The uniformly rigid generic fiber of a quasi-compact formal scheme of formally finite type is quasi-compact, and its global functions are bounded. We construct our new category by starting out from semi-affinoid algebras and nested rational coverings; we prove a uniformly rigid acyclicity theorem, and we study coherent modules. We then define formal Néron models for uniformly rigid spaces to be smooth formal schemes of formally finite type satisfying the universal Néron property. We establish the existence of formal Néron models for certain classes of uniformly rigid groups, and we discuss applications to Chai's program concerning the computation of the base change conductor for abelian varieties with potentially multiplicative reduction. This paper is a faithful copy of the author's doctoral thesis.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
