Split reductions of simple abelian varieties
Abstract
Consider an absolutely simple abelian variety X over a number field K. If the absolute endomorphism ring of X is commutative and satisfies certain parity conditions, then the reduction Xp is absolutely simple for almost all p. Conversely, if the absolute endomorphism ring of X is noncommutative, then Xp is reducible for p in a set of positive density.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.