A counterexample to the Gouvêa–Mazur conjecture
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چکیده
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. To cite this article: K. Buzzard, F. Calegari, C. R. Acad. Sci. Paris, Ser. I 338 (2004). 2004 Académie des sciences. Published by Elsevier SAS. All rights reserved. Résumé Un contre-exemple à la conjecture de Gouvêa–Mazur. 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. Pour citer cet article : K. Buzzard, F. Calegari, C. R. Acad. Sci. Paris, Ser. I 338 (2004). 2004 Académie des sciences. Published by Elsevier SAS. All rights reserved.
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