Author

Yu-Fan Luo

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Preprint Sep 2026

On Boston's Unramified Conjecture for $\GL_2$ and McLeman's $(3,3)$-Conjecture

Let $p$ be an odd prime number. Based on recent work of Zhang, we prove that for a finite set $S$ of primes of $\Q$ containing $\infty$ but not $p$, any continuous odd representation $G_{\Q,S} \to \GL_2(A)$ over a complete Noetherian local ring $A$ with finite residue field of characteristic $p$ has finite image, where...

Yu-Fan Luo · 0 citations

Preprint Sep 2026

On the bounded-conductor finiteness conjecture in equal characteristic

We investigate the equal-characteristic case of the Moon--Taguchi bounded-conductor finiteness conjecture for mod $p$ Galois representations over global function fields. We first establish a conditional finiteness theorem: for any global function field $K$ of characteristic $p$ and any integer $n \ge 1$, there are only...

Yu-Fan Luo, Yi-Qi Xu · 0 citations