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15 February 2020 Exceptional splitting of reductions of abelian surfaces
Ananth N. Shankar, Yunqing Tang
Duke Math. J. 169(3): 397-434 (15 February 2020). DOI: 10.1215/00127094-2019-0046

Abstract

Heuristics based on the Sato–Tate conjecture and the Lang–Trotter philosophy suggest that an abelian surface defined over a number field has infinitely many places of split reduction. We prove this result for abelian surfaces with real multiplication. As in previous work by Charles and Elkies, this shows that a density 0 set of primes pertaining to the reduction of abelian varieties is infinite. The proof relies on the Arakelov intersection theory on Hilbert modular surfaces.

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Ananth N. Shankar. Yunqing Tang. "Exceptional splitting of reductions of abelian surfaces." Duke Math. J. 169 (3) 397 - 434, 15 February 2020. https://doi.org/10.1215/00127094-2019-0046

Information

Received: 5 March 2018; Revised: 5 June 2019; Published: 15 February 2020
First available in Project Euclid: 11 December 2019

zbMATH: 07198458
MathSciNet: MR4065146
Digital Object Identifier: 10.1215/00127094-2019-0046

Subjects:
Primary: 11G05
Secondary: 11G18, 14G40

Rights: Copyright © 2020 Duke University Press

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Vol.169 • No. 3 • 15 February 2020
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