Analytification for Complex Geometry Revisited

We develop an ind-Banach framework for revisiting analytification in complex geometry, inspired by Bambozzi-Chiarellotto-Vanni’s work on tempered cohomology. We define several ind-Banach rings of overconvergent and holomorphic power series to endow $\mathbb{C}$-algebras with analytic structures. As an application, we obtain an abstract GAGA-type comparison in this setting.