Tag Archives: George Schaeffer

Polymath Proposal: 4-folds of Mumford’s type

Posted on August 24, 2021 by Persiflage

Let \(A/K\) be an abelian variety of dimension \(g\) over a number field. If \(g \not\equiv 0 \bmod 4\) and \(\mathrm{End}(A/\mathbf{C}) = \mathbf{Z}\), then Serre proved that the Galois representations associated to \(A\) have open image in \(\mathrm{GSp}_{2g}(\mathbf{Z}_p)\). The result … Continue reading →

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I asked… and you responded!

Posted on September 30, 2019 by Persiflage

I often ask mathematical questions on this blog that I don’t know how to answer. Sometimes my smart readers are able to answer the questions I ask. Surely they deserve some recognition for this? Here are two such occasions which … Continue reading →

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Gross Fugue

Posted on January 11, 2014 by Persiflage

Here are some variations on the theme of the last post, which is also related to a problem of Dick Gross. In this post, I want to discuss weight one modular forms where the level varies in the “vertical” aspect … Continue reading →

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The mystery of the primes

Posted on January 4, 2014 by Persiflage

No, this is not the sequel to Marcus du Sautoy’s book, but rather a curious observation regarding George Schaeffer’s tables of “ethereal” weight one Katz modular eigenforms (which you can find starting on p.64 here). Let \(N\) be a positive … Continue reading →

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