Geometric decomposition of abelian varieties of order 1

Toren D'Nelly-Warady, Kiran S. Kedlaya

Publication date: 8 September 2021

Abstract: 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

m a t h b b F_{2}

. We determine the decomposition of these varieties into simple factors over an algebraic closure of

m a t h b b F_{2}

; this requires solving a polynomial equation in three roots of unity.

Has companion code repository: https://github.com/mwarady22/geometric-decomposition-of-abelian-varieties-of-order-1

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