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

Yunqing Tang (1) , Jérémy Magnien (2)

1 Department of Mathematics - Princeton University
2 IF - Institut Fourier

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.

Mots clés: Arakelov Geometry and diophantine applications; reductions; abelian surfaces; multiplication

Mots clés: eem2017; Géométrie d'Arakelov et applications diophantiennes; Grenoble

Domaines: Mathématiques [math]

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⟩