Timeline for Class numbers of functions fields and spanning trees
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Jul 18, 2022 at 23:15 | history | edited | Antoine Labelle | CC BY-SA 4.0 |
Correct false claim
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| Jul 15, 2022 at 15:56 | comment | added | David E Speyer | But the graph $\Gamma$ for the modular curve isn't the isogeny graph; it is the graph with two vertices and $g+1$ edges between them, where $g \approx \tfrac{p}{24}$ is the genus of the modular curve. So I don't actually know if this is relevant to you. | |
| Jul 15, 2022 at 15:54 | comment | added | David E Speyer | Then there is an abelian group called $\text{Pic}^0(\Gamma)$ whose cardinality is the number of spanning trees of $\Gamma$, and there is a specialization map $\text{Pic}^0(X)(K) \to \text{Pic}^0(\Gamma)$. | |
| Jul 15, 2022 at 15:53 | comment | added | David E Speyer | I started to write up an answer pointing you to arxiv.org/abs/math/0701075 , but on reflection it isn't as relevant as I thought it was. So I'll make it a more brief comment. Let $R$ be a dvr and let $\mathcal{X}$ be a regular semistable curve over $\text{Spec}(R)$. Let $X$ be the general fiber and $X_0$ the special fiber. Let Let $\Gamma$ be the graph whose vertices are the components of $X_0$ and whose edges are the nodes of $X_0$. | |
| Jul 15, 2022 at 9:03 | history | became hot network question | |||
| Jul 15, 2022 at 1:44 | answer | added | Will Sawin | timeline score: 8 | |
| Jul 15, 2022 at 1:03 | history | asked | Antoine Labelle | CC BY-SA 4.0 |