The Manin constant in the semistable case
Number Theory
2019-02-20 v3
Abstract
For an optimal modular parametrization of an elliptic curve over of conductor , Manin conjectured the agreement of two natural -lattices in the -vector space . Multiple authors generalized his conjecture to higher dimensional newform quotients. We prove the Manin conjecture for semistable , give counterexamples to all the proposed generalizations, and prove several semistable special cases of these generalizations. The proofs establish general relations between the integral -adic etale and de Rham cohomologies of abelian varieties over -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