The large Galois orbits conjecture under multiplicative degeneration

2023/06/23 by Christopher Daw, Daw, Christopher, Martin Orr +1 · 3 citations
Arts and Humanities · Mathematics · Social Sciences · #11G18 #11G50 #14G22 #14G35 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Historical Studies and Socio-cultural Analysis #Number Theory (math.NT) #Vietnamese History and Culture Studies

paper · pdf · doi:10.48550/arxiv.2306.13463

openalex publication_date 2023/06/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish the PEL type large Galois orbits conjecture for Hodge generic curves in A_g possessing multiplicative degeneration. Combined with our earlier works, this concludes the proof of the Zilber-Pink conjecture in A₂ for such curves. We also deduce several new cases of Zilber-Pink in A_g for g≥ 3. Our proof uses André's G-functions method, using formal and rigid uniformisation of semiabelian schemes to interpret the p-adic evaluations of the period G-functions.

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