Bruno Chiarellotto, Fabien Trihan
Comptes Rendus. Mathématique 363(G9) 867-871 2025年7月15日 査読有り
In this paper, we apply Tsuzuki’s main theorem in [12] to establish a criterion for when two abelian varieties over a function field of characteristic are isogenous. Specifically, assuming that their endomorphism algebras tensored with are division algebras, we prove that if the maximal quotients of minimal slope (i.e., the unique maximal isoclinic quotient corresponding to the minimal slope, defined up to isogeny) of their associated -divisible groups are isogenous, then the abelian varieties themselves are isogenous over . We also extend this result to certain -divisible groups, highlighting the deep connection between isogenies of abelian varieties and the structure of overconvergent -isocrystals.