Séminaire de géométrie du 14 octobre 2026 à 14h - salle de conférences du CMLS

Title: Weight functions on the Berkovich affine line over any non-Archimedean field

 

Abstract: The theory of weight functions on Berkovich spaces hints at an intrinsic approach to studying skeleta without the limitations of the usual tools from algebraic geometry such as semistable reduction or resolution of singularities. We will discuss how weight functions can be intrinsically defined on any quasi-smooth Berkovich space. Next we will show that on the Berkovich affine line over any non-Archimedean field K, weight functions are completely determined by a certain kind of Z-PL structure and vice versa, yielding new insights into its Z-PL structure. Finally, we will discuss how this can be used to define and compute the essential skeleton of certain Berkovich spaces.