3 papers
math.NT2025
Topological adelic curves: Zariski-Riemann spaces, algebraic coverings, Harder-Narsimhan filtrations and heights
Antoine Sédillot
In this article, we introduce topological adelic curves. Roughly speaking, a topological adelic curve is a topological space of (generalised) absolute values on a given field satis…
math.NT2024
Pseudo-absolute values: foundations
Antoine Sédillot
In this article, we introduce pseudo-absolute values, which generalise usual absolute values. Roughly speaking, a pseudo-absolute value on a field is a map $|\cdot| : K \to [0,…
math.AG2023
Differentiability of the -volume function over an adelic curve
Antoine Sédillot
In this article, we show a differentiability property for the -volume function on the ample cone of adelic line bundles over an adelic curve. This result is deduced from a non-A…