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Dill, Gabriel Andreas

Nom
Dill, Gabriel Andreas
Affiliation principale
Site web
Email
gabriel.dill@unine.ch
Identifiants
https://libra.unine.ch/handle/123456789/33097
_
0000-0002-1635-5792

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  • Publication
    Accès libre
    Distinguished Categories and the Zilber-Pink Conjecture
    (2025)
    Fabrizio Barroero
    ;
    Dill, Gabriel Andreas 
    We propose an axiomatic approach towards studying unlikely intersections by introducing the framework of distinguished categories. This includes commutative algebraic groups and mixed Shimura varieties. It allows us to define all basic concepts of the field and to prove some fundamental facts about them, e.g., the defect condition. In some categories that we call very distinguished, we are able to show some implications between Zilber-Pink statements with respect to base change. This yields unconditional results, i.e., the Zilber-Pink conjecture for a complex curve in $\mathcal{A}_2$ that cannot be defined over $\bar{\mathbb{Q}}$, a complex curve in the g-th fibered power of the Legendre family, and a complex curve in the base change of a semiabelian variety over $\bar{\mathbb{Q}}$.
  • Publication
    Accès libre