Cesar Hilario ; Stefan Schröer - Generalizations of quasielliptic curves

epiga:11181 - Épijournal de Géométrie Algébrique, January 8, 2024, Volume 7 - https://doi.org/10.46298/epiga.2024.11181
Generalizations of quasielliptic curvesArticle

Authors: Cesar Hilario ; Stefan Schröer

    We generalize the notion of quasielliptic curves, which have infinitesimal symmetries and exist only in characteristic two and three, to a remarkable hierarchy of regular curves having infinitesimal symmetries, defined in all characteristics and having higher genera. This relies on the study of certain infinitesimal group schemes acting on the affine line and certain compactifications. The group schemes are defined in terms of invertible additive polynomials over rings with nilpotent elements, and the compactification is constructed with the theory of numerical semigroups. The existence of regular twisted forms relies on Brion's recent theory of equivariant normalization. Furthermore, extending results of Serre from the realm of group cohomology, we describe non-abelian cohomology for semidirect products, to compute in special cases the collection of all twisted forms.

    Volume: Volume 7
    Published on: January 8, 2024
    Accepted on: September 29, 2023
    Submitted on: April 12, 2023
    Keywords: Mathematics - Algebraic Geometry,14G17, 14L15, 14L30, 14H45, 20M25, 20J06, 14D06

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