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Torsion points of elliptic curves via Berkovich spaces over $\mathbb{Z}$

By Jerôme Poineau

Appears in collection : Global invariants of arithmetic varieties / Invariants globaux des variétés arithmétiques

Berkovich spaces over $\mathbb{Z}$ may be seen as fibrations containing complex analytic spaces as well as $p$-adic analytic spaces, for every prime number $p$. We will give an introduction to those spaces and explain how they may be used in an arithmetic context to prove height inequalities. As an application, following a strategy by DeMarco-Krieger-Ye, we will give a proof of a conjecture of Bogomolov-Fu-Tschinkel on uniform bounds on the number of common images on P1 of torsion points of two elliptic curves.

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  • DOI 10.24350/CIRM.V.20102203
  • Cite this video Poineau Jerôme (10/12/23). Torsion points of elliptic curves via Berkovich spaces over $\mathbb{Z}$. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20102203
  • URL https://dx.doi.org/10.24350/CIRM.V.20102203

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