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Mathematics > Algebraic Geometry

arXiv:1812.11694 (math)
This paper has been withdrawn by Jun Yong Park
[Submitted on 31 Dec 2018 (v1), last revised 7 Jul 2022 (this version, v9)]

Title:$\ell$-adic étale cohomology of the moduli of stable elliptic fibrations

Authors:Jun-Yong Park
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Abstract:We determine the $\ell$-adic étale cohomology and the eigenvalues of the geometric Frobenius for the moduli stack $\mathcal{L}_{1,12n} := \mathrm{Hom}_{n}(\mathbb{P}^1, \overline{\mathcal{M}}_{1,1})$ of stable elliptic fibrations over $\mathbb{P}^{1}$ with $12n$ nodal singular fibers and a marked Weierstrass section over $\overline{\mathbb{F}}_q$ with $\mathrm{char}(\overline{\mathbb{F}}_q) \neq 2,3$.
Comments: This paper is superseded by a newer paper, entitled "Étale cohomological stability of the moduli space of stable elliptic surfaces" arXiv:2207.02496 (by O. Banerjee, J. Park, and J. Schmitt)
Subjects: Algebraic Geometry (math.AG); Algebraic Topology (math.AT); Number Theory (math.NT)
Cite as: arXiv:1812.11694 [math.AG]
  (or arXiv:1812.11694v9 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1812.11694

Submission history

From: Jun Yong Park [view email]
[v1] Mon, 31 Dec 2018 04:08:47 UTC (8 KB)
[v2] Thu, 3 Jan 2019 08:14:31 UTC (8 KB)
[v3] Sun, 3 Feb 2019 03:47:00 UTC (8 KB)
[v4] Thu, 6 Jun 2019 11:28:57 UTC (11 KB)
[v5] Sun, 28 Jul 2019 02:51:40 UTC (11 KB)
[v6] Thu, 23 Jan 2020 04:48:13 UTC (11 KB)
[v7] Fri, 15 May 2020 08:05:24 UTC (11 KB)
[v8] Mon, 13 Jul 2020 07:19:23 UTC (11 KB)
[v9] Thu, 7 Jul 2022 14:24:34 UTC (1 KB) (withdrawn)
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