A counterexample to the Gouvêa–Mazur conjecture

Kevin Buzzard; Frank Calegari

doi:10.1016/j.crma.2004.03.016

Number Theory

A counterexample to the Gouvêa–Mazur conjecture

Presented by: Christophe Soulé

Kevin Buzzard ¹; Frank Calegari ²

¹ Department of Mathematics, Imperial College, 180, Queen's Gate, London SW7 2AZ, UK
² 1, Science Center, Department of Mathematics, Harvard University, Cambridge, MA 02138, USA

Comptes Rendus. Mathématique, Volume 338 (2004) no. 10, pp. 751-753.

Abstract
Résumé

Gouvêa and Mazur made a precise conjecture about slopes of modular forms. Weaker versions of this conjecture were established by Coleman and Wan. In this Note, we exhibit examples contradicting the full conjecture as it currently stands.

Gouvêa et Mazur ont proposé une conjecture précise au sujet des pentes des formes modulaires. Des versions plus faibles de cette conjecture ont été prouvées par Coleman et Wan. Dans cette Note, nous exhibons des exemples contredisant la conjecture.

Received: 2004-03-04
Accepted: 2004-03-16
Published online: 2004-04-09

DOI: 10.1016/j.crma.2004.03.016

Author's affiliations:

Kevin Buzzard ¹; Frank Calegari ²

¹ Department of Mathematics, Imperial College, 180, Queen's Gate, London SW7 2AZ, UK
² 1, Science Center, Department of Mathematics, Harvard University, Cambridge, MA 02138, USA

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Kevin Buzzard; Frank Calegari. A counterexample to the Gouvêa–Mazur conjecture. Comptes Rendus. Mathématique, Volume 338 (2004) no. 10, pp. 751-753. doi : 10.1016/j.crma.2004.03.016. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.03.016/

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