Siksek, Samir (2022) Integral points on punctured abelian varieties. European Journal of Mathematics, 8 . pp. 687-703. doi:10.1007/s40879-022-00570-4 ISSN 2199-675X.

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Abstract

Let A/Q be an abelian variety such that A(Q)={0A}. Let ℓ and p be rational primes, such that A has good reduction at p, and satisfying ℓ≡1(modp) and ℓ∤#A(Fp). Let S be a finite set of rational primes. We show that (A∖{0A})(OL,S)=∅ for 100% of cyclic degree ℓ fields L/Q, when ordered by conductor, or by absolute discriminant.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH):	Abelian varieties, Number theory, Integral equations, Algebra
Journal or Publication Title:	European Journal of Mathematics
Publisher:	Springer
ISSN:	2199-675X
Official Date:	November 2022
Dates:	Date Event November 2022 Published 30 August 2022 Available 13 July 2022 Accepted
Volume:	8
Page Range:	pp. 687-703
DOI:	10.1007/s40879-022-00570-4
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access (Creative Commons)
Date of first compliant deposit:	19 July 2022
Date of first compliant Open Access:	31 August 2022
RIOXX Funder/Project Grant:	Project/Grant ID RIOXX Funder Name Funder ID EP/S031537/1 [EPSRC] Engineering and Physical Sciences Research Council http://dx.doi.org/10.13039/501100000266
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