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A counterexample to the Gouvea--Mazur conjecture

Kevin Buzzard·Frank Calegari
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Abstract

Gouvea 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 explicit examples contradicting the full conjecture as it currently stands.

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Kevin Buzzard, Frank Calegari. 2003-11-20. A counterexample to the Gouvea--Mazur conjecture. https://arxiv.org/abs/math/0311361

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