2025/01/01 by Gao, Ziyang, Habegger, Philipp
Mathematics · #510 #Abelian schemes #Algebraic Geometry and Number Theory #Bi-algebraic subvarieties #Commutative Algebra and Its Applications #Degeneracy loci #Geometry and complex manifolds #Relative Manin–Mumford #Uniform Mordell–Lang
paper · doi:10.15488/19938
openalex publication_date 2025/01/01 · openalex created_date 2025/11/07 · openalex updated_date 2026/07/01
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.