Papers › Geometric decomposition of abelian varieties of order 1
Geometric decomposition of abelian varieties of order 1
Toren D'Nelly-Warady, Kiran S. Kedlaya
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Since the 1970s, the complete classification (up to isogeny) of abelian varieties over finite fields with trivial group of rational points has been known from results of Madan--Pal and Robinson; with two exceptions these are all defined over 𝔽₂. We determine the decomposition of these varieties into simple factors over an algebraic closure of 𝔽₂; this requires solving a polynomial equation in three roots of unity.
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