Surjectivity of Galois representations in rational families of abelian varieties
| Autor: | James Tao, Aaron Landesman, Yujie Xu, Ashvin Swaminathan |
|---|---|
| Přispěvatelé: | Lombardo, Davide |
| Rok vydání: | 2019 |
| Předmět: |
Abelian variety
Pure mathematics 11F80 Plane curve Mathematics::Number Theory big monodromy Group Theory (math.GR) 01 natural sciences 11N36 11R32 Mathematics - Algebraic Geometry Mathematics::Algebraic Geometry 0103 physical sciences FOS: Mathematics Number Theory (math.NT) Representation Theory (math.RT) Galois representation 0101 mathematics Abelian group Algebraic Geometry (math.AG) Mathematics Algebra and Number Theory Mathematics - Number Theory 11G30 abelian variety Hilbert irreducibility theorem 11G10 Image (category theory) 12E25 010102 general mathematics 11F80 11G10 11R32 11G30 12E25 11N36 Galois module Base (topology) Étale fundamental group étale fundamental group Monodromy 010307 mathematical physics Mathematics - Group Theory Mathematics - Representation Theory large sieve |
| Zdroj: | Algebra Number Theory 13, no. 5 (2019), 995-1038 |
| ISSN: | 1944-7833 1937-0652 |
| DOI: | 10.2140/ant.2019.13.995 |
| Popis: | In this article, we show that for any non-isotrivial family of abelian varieties over a rational base with big monodromy, those members that have adelic Galois representation with image as large as possible form a density-$1$ subset. Our results can be applied to a number of interesting families of abelian varieties, such as rational families dominating the moduli of Jacobians of hyperelliptic curves, trigonal curves, or plane curves. As a consequence, we prove that for any dimension $g \geq 3$, there are infinitely many abelian varieties over $\mathbb Q$ with adelic Galois representation having image equal to all of $\operatorname{GSp}_{2g}(\widehat{\mathbb Z})$. 41 pages |
| Databáze: | OpenAIRE |
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