The large Galois orbits conjecture under multiplicative degeneration
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866910945801928704 |
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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 |