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arXiv · 2605.31403

The Bogomolov property for $p$-supercuspidal eigenforms

Andrea Conti·Pietro Piras·Lea Terracini
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Abstract

We prove a lower bound on the Weil height, the so-called Bogomolov property, for the algebraic extensions of $\mathbb Q$ cut out by the adelic Galois representations attached to certain eigenforms whose local component at a prime $p$ is supercuspidal. To this end, we give a method for constructing metric inequalities over $p$-adic Lie extensions of fields over $\mathbb Q$ that are finitely ramified at $p$.

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BibTeXRIS

Andrea Conti, Pietro Piras, Lea Terracini. 2026-05-29. The Bogomolov property for $p$-supercuspidal eigenforms. https://arxiv.org/abs/2605.31403

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