Abelian varieties with real multiplication: classification and isogeny classes over finite fields

Abstract

In this paper, we provide a classification of certain points on Hilbert modular varieties over finite fields under a mild assumption on Newton polygon. Furthermore, we use this characterization to prove estimates for the size of isogeny classes.

Fixed typos and accommodated referee comments. Minor changes in the proof of Proposition 3.2 and Lemma 3.6