On the proportion of metric matroids whose Jacobians have nontrivial $\mathbf{p}$-torsion
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866909649379262464 |
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| author | Ceballos, Sergio Ricardo Zapata |
| author_facet | Ceballos, Sergio Ricardo Zapata |
| contents | We study the proportion of metric matroids whose Jacobians have nontrivial $p$-torsion. We establish a correspondence between these Jacobians and the $\mathbb{F}_p$-rational points on configuration hypersurfaces, thereby relating their proportions. By counting points over finite fields, we prove that the proportion of these Jacobians is asymptotically equivalent to $1/p$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_10172 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the proportion of metric matroids whose Jacobians have nontrivial $\mathbf{p}$-torsion Ceballos, Sergio Ricardo Zapata Combinatorics Number Theory 11G25, 14G05, 14N20, 60B99, 05C31, 05C50, 05C76, 14M12, 81Q30 We study the proportion of metric matroids whose Jacobians have nontrivial $p$-torsion. We establish a correspondence between these Jacobians and the $\mathbb{F}_p$-rational points on configuration hypersurfaces, thereby relating their proportions. By counting points over finite fields, we prove that the proportion of these Jacobians is asymptotically equivalent to $1/p$. |
| title | On the proportion of metric matroids whose Jacobians have nontrivial $\mathbf{p}$-torsion |
| topic | Combinatorics Number Theory 11G25, 14G05, 14N20, 60B99, 05C31, 05C50, 05C76, 14M12, 81Q30 |
| url | https://arxiv.org/abs/2306.10172 |