Details
| Original language | English |
|---|---|
| Number of pages | 26 |
| Journal | Journal of number theory |
| Early online date | 27 Jun 2024 |
| Publication status | E-pub ahead of print - 27 Jun 2024 |
Abstract
Recent developments on the uniformity of the number of rational points on curves and subvarieties in a moving abelian variety rely on the geometric concept of the degeneracy locus. The first-named author investigated the degeneracy locus in certain mixed Shimura varieties. In this expository note we revisit some of these results while minimizing the use of mixed Shimura varieties while working in a family of principally polarized abelian varieties. We also explain their relevance for applications in diophantine geometry.
Keywords
- Abelian schemes, Bi-algebraic subvarieties, Degeneracy loci, Relative Manin–Mumford, Uniform Mordell–Lang
ASJC Scopus subject areas
- Mathematics(all)
- Algebra and Number Theory
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In: Journal of number theory, 27.06.2024.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Degeneracy loci in the universal family of Abelian varieties
AU - Gao, Ziyang
AU - Habegger, Philipp
N1 - Publisher Copyright: © 2024 The Author(s)
PY - 2024/6/27
Y1 - 2024/6/27
N2 - Recent developments on the uniformity of the number of rational points on curves and subvarieties in a moving abelian variety rely on the geometric concept of the degeneracy locus. The first-named author investigated the degeneracy locus in certain mixed Shimura varieties. In this expository note we revisit some of these results while minimizing the use of mixed Shimura varieties while working in a family of principally polarized abelian varieties. We also explain their relevance for applications in diophantine geometry.
AB - Recent developments on the uniformity of the number of rational points on curves and subvarieties in a moving abelian variety rely on the geometric concept of the degeneracy locus. The first-named author investigated the degeneracy locus in certain mixed Shimura varieties. In this expository note we revisit some of these results while minimizing the use of mixed Shimura varieties while working in a family of principally polarized abelian varieties. We also explain their relevance for applications in diophantine geometry.
KW - Abelian schemes
KW - Bi-algebraic subvarieties
KW - Degeneracy loci
KW - Relative Manin–Mumford
KW - Uniform Mordell–Lang
UR - http://www.scopus.com/inward/record.url?scp=85197300471&partnerID=8YFLogxK
U2 - 10.1016/j.jnt.2024.05.015
DO - 10.1016/j.jnt.2024.05.015
M3 - Article
AN - SCOPUS:85197300471
JO - Journal of number theory
JF - Journal of number theory
SN - 0022-314X
ER -