Tag Archives: Weight one forms

A non-liftable weight one form modulo p^2

Posted on March 10, 2017 by Persiflage

I once idly asked RLT (around 2004ish) whether one could use Buzzard-Taylor arguments to prove that any representation: \(\rho: \mathrm{Gal}(\overline{\mathbf{Q}}/\mathbf{Q}) \rightarrow \mathrm{GL}_2(\mathbf{Z}/p^2 \mathbf{Z})\) which was unramified at p and residually irreducible (and modular) was itself modular (in the Katz sense). … Continue reading →

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There are non-liftable weight one forms modulo p for any p

Posted on June 10, 2014 by Persiflage

Let \(p\) be any prime. In this post, we show that there is an integer \(N\) prime to \(p\) such that \(H^1(X_1(N),\omega_{\mathbf{Z}})\) has a torsion class of order \(p\). Almost equivalently, there exists a Katz modular form of level \(N\) … Continue reading →

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