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Skeletal filtrations of the fundamental group of a non-archimedean curve (2023)
Journal Article
Helminck, P. A. (2023). Skeletal filtrations of the fundamental group of a non-archimedean curve. Advances in Mathematics, 431, Article 109242. https://doi.org/10.1016/j.aim.2023.109242

In this paper we study skeleta of residually tame coverings of a marked curve over a non-archimedean field. We first prove a simultaneous semistable reduction theorem for residually tame coverings, which we then use to construct a tropicalization fun... Read More about Skeletal filtrations of the fundamental group of a non-archimedean curve.

Invariants for trees of non-archimedean polynomials and skeleta of superelliptic curves (2022)
Journal Article
Helminck, P. A. (2022). Invariants for trees of non-archimedean polynomials and skeleta of superelliptic curves. Mathematische Zeitschrift, 301(2), 1259-1297. https://doi.org/10.1007/s00209-021-02959-5

In this paper we generalize the j-invariant criterion for the semistable reduction type of an elliptic curve to superelliptic curves X given by yn=f(x). We first define a set of tropical invariants for f(x) using symmetrized Plücker coordinates and w... Read More about Invariants for trees of non-archimedean polynomials and skeleta of superelliptic curves.