Institut de Mathématiques de Marseille, UMR 7373


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Arithmetic hyperbolicity

Mardi 14 février 11:00-12:00 - Ariyan JAVANPEYKAR - Mainz

Arithmetic hyperbolicity

Résumé : We will show that, assuming Lang-Vojta’s conjecture, the moduli of smooth hypersurfaces of fixed degree in a fixed projective space is arithmetically hyperbolic. More generally, any algebraic stack with an immersive period map is arithmetically hyperbolic assuming Lang-Vojta’s conjecture.
We finish with unconditional results. For instance, we verify the arithmetic hyperbolicity of the moduli of smooth sextic surfaces, and certain Fano threefolds. We also give a first explicit counterexample to Shafarevich’s problem for Fano threefolds.
This is joint work with Daniel Loughran.

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Lieu : CMI, salle C003

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