Preston Wake

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math.NT2025

The Eisenstein ideal at prime-square level has constant rank

Jaclyn Lang, Preston Wake

Let $N$ and $p$ be prime numbers with $p \geq 5$ such that $p ∣∣ (N + 1)$ . In a previous paper, we showed that there is a cuspform $f$ of weight 2 and level $I^_{0} (N^{2})$ whose $\ell…

math.NT2024

Explicit non-Gorenstein R=T via rank bounds I: Deformation theory

Catherine Hsu, Preston Wake, Carl Wang-Erickson

Ribet has proven remarkable results about non-optimal levels of residually reducible Galois representations. We focus on a non-optimal level $N$ that is the product of two distinct…