Timeline for Is the unipotent section map of hyperbolic curve over local field injective?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Apr 5, 2022 at 22:58 | comment | added | Alexander Betts | The corresponding result for the pro-p fundamental group is at least true, and is a theorem of Mochizuki (Theorem C of The Local Pro-p Anabelian Geometry of Curves). | |
| Mar 3, 2021 at 1:50 | comment | added | David Corwin | It's actually not too hard to cook up an example where the map $X(\mathbb{Z}_p) \to H^1(G_{\mathbb{Q}_p},\pi_1^{un}(J_{\overline{\mathbb{Q}_p}},b)) = H^1(G_{\mathbb{Q}_p},\pi_1^{un}(X_{\overline{\mathbb{Q}_p}},b)^{ab})$ is not injective. | |
| Mar 3, 2021 at 1:49 | comment | added | David Corwin | Let $J$ be the Jacobian of $X$. Then it's clear that the map from $X$ to $J$ is injective, and the map from $J$ to $H^1(G_{\mathbb{Q}_p},\pi_1^{un}(J_{\overline{\mathbb{Q}_p}},b))$ is injective modulo torsion. But it does seem more tricky to prove that the map on $X(\mathbb{Z}_p)$ is injective. | |
| Feb 24, 2021 at 6:14 | history | edited | Francesco Polizzi | CC BY-SA 4.0 |
added 29 characters in body
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| Feb 24, 2021 at 5:30 | history | asked | Heavensfall | CC BY-SA 4.0 |