Vol. 9, No. 1, 2015

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Categories of abelian varieties over finite fields, I: Abelian varieties over $\mathbb{F}_{p}$

Tommaso Giorgio Centeleghe and Jakob Stix

Vol. 9 (2015), No. 1, 225–265

We assign functorially a -lattice with semisimple Frobenius action to each abelian variety over Fp. This establishes an equivalence of categories that describes abelian varieties over Fp avoiding p as an eigenvalue of the Frobenius in terms of simple commutative algebra. This result extends the isomorphism classification of Waterhouse and Deligne’s equivalence for ordinary abelian varieties.

abelian varieties, finite fields, Gorenstein rings, reflexive modules
Mathematical Subject Classification 2010
Primary: 11-02
Received: 21 July 2014
Revised: 5 December 2014
Accepted: 6 January 2015
Published: 18 February 2015
Tommaso Giorgio Centeleghe
Universität Heidelberg
Im Neuenheimer Feld 368
D-69120 Heidelberg
Jakob Stix
Institut fĂĽr Mathematik
Goethe-Universität Frankfurt
Robert-Mayer-Straße 6–8
D-60325 Frankfurt am Main