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1 December 2018 How large is Ag(Fq)?
Michael Lipnowski, Jacob Tsimerman
Duke Math. J. 167(18): 3403-3453 (1 December 2018). DOI: 10.1215/00127094-2018-0029

Abstract

Let B(g,p) denote the number of isomorphism classes of g-dimensional Abelian varieties over the finite field of size p. Let A(g,p) denote the number of isomorphism classes of principally polarized g-dimensional Abelian varieties over the finite field of size p. We derive upper bounds for B(g,p) and lower bounds for A(g,p) for p fixed and g increasing. The extremely large gap between the lower bound for A(g,p) and the upper bound for B(g,p) implies some statistically counterintuitive behavior for Abelian varieties of large dimension over a fixed finite field.

Citation

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Michael Lipnowski. Jacob Tsimerman. "How large is Ag(Fq)?." Duke Math. J. 167 (18) 3403 - 3453, 1 December 2018. https://doi.org/10.1215/00127094-2018-0029

Information

Received: 10 December 2015; Revised: 7 March 2018; Published: 1 December 2018
First available in Project Euclid: 15 November 2018

zbMATH: 07009769
MathSciNet: MR3881200
Digital Object Identifier: 10.1215/00127094-2018-0029

Subjects:
Primary: 11G10
Secondary: 11G25

Rights: Copyright © 2018 Duke University Press

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Vol.167 • No. 18 • 1 December 2018
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