On the Existence of Absolutely Simple Abelian Varieties of a Given Dimension over an Arbitrary Field

By Everett W. Howe, Hui June Zhu. 2000

74 citations recorded by the source corpus.

Abstract We prove that for every field k and every positive integer n there exists an absolutely simple n -dimensional abelian variety over k . We also prove an asymptotic result for finite fields: For every finite field k and positive integer n , we let S ( k ,  n ) denote the fraction of the isogeny classes of n -dimensional abelian varieties over k that consist of absolutely simple ordinary abelian varieties. Then for every n we have S ( F q ,  n )→1 as q →∞ over the prime powers.

Subfields: Artificial Intelligence, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/2c64290b14815983de2bf384b6dffdbe76233404

How researchers see this paper

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In Artificial Intelligence

1. R. Pries
2. Chris Hall

In Discrete Mathematics and Combinatorics

1. R. Pries
2. Jeff Achter

In Geometry and Topology

1. R. Pries
2. Jeff Achter
3. Chris Hall

Citations in the corpus

• The integral monodromy of hyperelliptic and trielliptic curves (2006, background): “Related work can be found in [15] where the authors produce curves with absolutely simple Jacobians over Fp under the restriction g ≤ 3.”