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Archivio digitale delle tesi discusse presso l’Università di Pisa

Tesi etd-01102024-164015


Tipo di tesi
Tesi di laurea magistrale
Autore
COLPO, DAVIDE
URN
etd-01102024-164015
Titolo
Toric Manin-Mumford via Raynaud's method
Dipartimento
MATEMATICA
Corso di studi
MATEMATICA
Relatori
relatore Prof. Lombardo, Davide
correlatore Prof. Zannier, Umberto
controrelatore Prof. Talpo, Mattia
Parole chiave
  • algebraic tori
  • arithmetic geometry
  • Manin-Mumford
  • torsion points
Data inizio appello
26/01/2024
Consultabilità
Completa
Riassunto
The Manin-Mumford conjecture states that if X is a proper, integral curve over C of geometric genus at least 2, embedded in a C-abelian variety A, then X contains at most finitely many C-torsion points of A.
The purpose of this thesis is to adapt Raynaud’s proof [Inventiones Mathematicae, n.71 (1983), pp. 207-233] of the Manin-Mumford conjecture to the toric case. We define a torsion coset of a group to be a left translate of a subgroup by a torsion element.
We will prove the following: if X is a smooth closed algebraic curve in (C^*)^n and none of its connected components is a torsion coset, then X contains at most finitely many torsion points of (C^*)^n .
Many proofs of this result are known, but, as far as we know, none of them
relies on Raynaud’s approach.
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