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Vidéo Année : 2017

Y. Tang - Exceptional splitting of reductions of abelian surfaces with real multiplication

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Jérémy Magnien
  • Fonction : Réalisateur
  • PersonId : 966327

Résumé

Chavdarov and Zywina showed that after passing to a suitable field extension, every abelian surface A with real multiplication over some number field has geometrically simple reduction modulo p for a density one set of primes p. One may ask whether its complement, the density zero set of primes p such that the reduction of A modulo p is not geometrically simple, is infinite. Such question is analogous to the study of exceptional mod p isogeny between two elliptic curves in the recent work of Charles. In this talk, I will discuss how to apply Charles's method to the setting of certain abelian surfaces with real multiplication. This is joint work with Ananth Shankar.

Dates et versions

medihal-01721490 , version 1 (02-03-2018)

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  • HAL Id : medihal-01721490 , version 1

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Yunqing Tang, Jérémy Magnien. Y. Tang - Exceptional splitting of reductions of abelian surfaces with real multiplication: Summer School 2017 - Arakelov Geometry and diophantine applications. 2017. ⟨medihal-01721490⟩
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