Special Cases of the Shafarevich Conjecture for Complete Intersections in Abelian Varieties

2025/06/17 by Frank Lu, Lu, Frank
Computer Science · Mathematics · #Coding theory and cryptography #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2506.14935

openalex publication_date 2025/06/17 · openalex created_date 2025/10/19 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove the Shafarevich conjecture for certain complete intersections of hypersurfaces in abelian varieties defined over a number field K using the Lawrence-Venkatesh method. The main new inputs we need are computation of certain Euler characteristics of these complete intersections and a big monodromy statement for the variation of Hodge structure arising from the middle cohomology of a family of such complete intersections. Following \citels25, we prove the latter by relating this monodromy statement to a statement about Tannaka groups, which we then convert into a combinatorial statement.

Related

• The Shafarevich conjecture for hypersurfaces in abelian varieties
• Complete intersections: Moduli, Torelli, and good reduction
• Shafarevich's conjecture for families of hypersurfaces over function fields
• Convolution monodromy groups and the Shafarevich conjecture for hypersurfaces in tori
• The Shafarevich conjecture for varieties with globally generated cotangent