The Manin constant in the semistable case

  title={The Manin constant in the semistable case},
  author={Kestutis Cesnavicius},
  journal={Compositio Mathematica},
  pages={1889 - 1920}
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… Expand
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