走向范畴凯勒几何
Towards Categorical Kähler Geometry
AI总结：
该研究在导出非交换几何框架下，提出阿基米德与非阿基米德情形中含BPS不等式等要素的凯勒度量理论，通过多类范畴与代数的例子构建相关研究框架。
AI中文摘要：
我们概述了导出非交换几何中凯勒度量这一新兴理论的轮廓，该理论是布里奇兰德稳定性条件理论的细化，编码了潜在的微分几何结构。我们在阿基米德和非阿基米德两种情形下提出了此类结构的要素，包括赋距对象、满足BPS不等式的质量测度、调和度量、极小化流以及复化凯勒势。我们通过涉及Fukaya范畴、箭图表示及相关C*-代数、谱网络、稳定∞-范畴的余单子伴随等的例子和构造来发展该框架。
英文摘要：
We outline the contours of an emerging theory of Kähler metrics in derived noncommutative geometry. This is a refinement of the theory of Bridgeland stability conditions encoding underlying differential-geometric structures. We propose elements of such a structure in both Archimedean and non-Archimedean settings, including metrized objects, mass measures satisfying a BPS inequality, harmonic metrics, minimizing flows, and complexified Kähler potentials. We develop the framework through examples and constructions involving Fukaya categories, quiver representations and associated C$^*$-algebras, spectral networks, and comonadic adjunctions of stable $\infty$-categories.
