The large Galois orbits conjecture under multiplicative degeneration

Fuente: arXiv
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Autori principali: Daw, Christopher, Orr, Martin
Natura: Preprint
Pubblicazione: 2023
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author Daw, Christopher
Orr, Martin
author_facet Daw, Christopher
Orr, Martin
contents We establish the PEL type large Galois orbits conjecture for Hodge generic curves in $\mathcal{A}_g$ possessing multiplicative degeneration. Combined with our earlier works, this concludes the proof of the Zilber-Pink conjecture in $\mathcal{A}_2$ for such curves. We also deduce several new cases of Zilber-Pink in $\mathcal{A}_g$ for $g\geq 3$. 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.
format Preprint
id arxiv_https___arxiv_org_abs_2306_13463
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle The large Galois orbits conjecture under multiplicative degeneration
Daw, Christopher
Orr, Martin
Number Theory
Algebraic Geometry
11G18, 11G50, 14G35, 14G22
We establish the PEL type large Galois orbits conjecture for Hodge generic curves in $\mathcal{A}_g$ possessing multiplicative degeneration. Combined with our earlier works, this concludes the proof of the Zilber-Pink conjecture in $\mathcal{A}_2$ for such curves. We also deduce several new cases of Zilber-Pink in $\mathcal{A}_g$ for $g\geq 3$. 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.
title The large Galois orbits conjecture under multiplicative degeneration
topic Number Theory
Algebraic Geometry
11G18, 11G50, 14G35, 14G22
url https://arxiv.org/abs/2306.13463