English

The Manin constant in the semistable case

Number Theory 2019-02-20 v3

Abstract

For an optimal modular parametrization J0(n)EJ_0(n) \twoheadrightarrow E of an elliptic curve EE over Q\mathbb{Q} of conductor nn, Manin conjectured the agreement of two natural Z\mathbb{Z}-lattices in the Q\mathbb{Q}-vector space H0(E,Ω1)H^0(E, \Omega^1). Multiple authors generalized his conjecture to higher dimensional newform quotients. We prove the Manin conjecture for semistable EE, give counterexamples to all the proposed generalizations, and prove several semistable special cases of these generalizations. The proofs establish general relations between the integral pp-adic etale and de Rham cohomologies of abelian varieties over pp-adic fields and exhibit a new exactness result for Neron models.

Keywords

Cite

@article{arxiv.1703.02951,
  title  = {The Manin constant in the semistable case},
  author = {Kestutis Cesnavicius},
  journal= {arXiv preprint arXiv:1703.02951},
  year   = {2019}
}

Comments

28 pages; final version, to appear in Compositio Mathematica

R2 v1 2026-06-22T18:40:00.660Z