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Abelian varieties over finite fields

Frans Jeroen Oort

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Abstract

Abstract. A. Weil proved that the geometric Frobenius π = F a of an abelian variety over a finite field with q = p a elements has absolute value q for every embedding. T. Honda and J. Tate showed that A ↦ → πA gives a bijection between the set of isogeny classes of simple abelian varieties over Fq and the set of conjugacy classes of q-Weil numbers. Higher-dimensional varieties over finite fields, Summer school in Göttingen, June 2007

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Abstract. A. Weil proved that the geometric Frobenius π = F a of an abelian variety over a finite field with q = p a elements has absolute value q for every embedding. T. Honda and J. Tate showed that A ↦ → πA gives a bijection between the set of isogeny classes of simple abelian varieties over Fq and the set of conjugacy classes of q-Weil numbers. Higher-dimensional varieties over finite fields, Summer school in Göttingen, June 2007

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Available abstract

Abstract. A. Weil proved that the geometric Frobenius π = F a of an abelian variety over a finite field with q = p a elements has absolute value q for every embedding. T. Honda and J. Tate showed that A ↦ → πA gives a bijection between the set of isogeny classes of simple abelian varieties over Fq and the set of conjugacy classes of q-Weil numbers. Higher-dimensional varieties over finite fields, Summer school in Göttingen, June 2007

Key concepts: Abelian group, Arithmetic of abelian varieties, Abelian variety, Mathematics, Abelian variety of CM-type, Rank of an abelian group, Finite field, Elementary abelian group

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