The Manin constant in the semistable case
2018 ◽
Vol 154
(9)
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pp. 1889-1920
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Keyword(s):
De Rham
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For an optimal modular parametrization $J_{0}(n){\twoheadrightarrow}E$ of an elliptic curve $E$ over $\mathbb{Q}$ of conductor $n$, Manin conjectured the agreement of two natural $\mathbb{Z}$-lattices in the $\mathbb{Q}$-vector space $H^{0}(E,\unicode[STIX]{x1D6FA}^{1})$. Multiple authors generalized his conjecture to higher-dimensional newform quotients. We prove the Manin conjecture for semistable $E$, give counterexamples to all the proposed generalizations, and prove several semistable special cases of these generalizations. The proofs establish general relations between the integral $p$-adic étale and de Rham cohomologies of abelian varieties over $p$-adic fields and exhibit a new exactness result for Néron models.
2018 ◽
Vol 154
(5)
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pp. 934-959
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2019 ◽
Vol 15
(09)
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pp. 1801-1826
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Keyword(s):
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Keyword(s):
Keyword(s):
2016 ◽
Vol 55
(3)
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pp. 401-427
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