Tag Archives: Inverse Galois Problem

Chidambaram on Galois representations (not) associated to abelian varieties over Q

Posted on October 13, 2020 by Persiflage

Today’s post is about a new paper by my student Shiva. Suppose that \(A/\mathbf{Q}\) is a principally polarized abelian variety of dimension \(g\) and \(p\) is a prime. The Galois representation on the \(p\)-torsion points \(A[p]\) gives rise to a … Continue reading →

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Dembélé on Abelian Surfaces with good reduction everywhere

Posted on March 27, 2019 by Persiflage

New paper by Dembélé (friend of the blog) on abelian surfaces with good reduction everywhere (or rather, the lack of them for many real quadratic fields of small discriminant). I have nothing profound to say about the question of which … Continue reading →

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Central Extensions, Updated

Posted on January 15, 2017 by Persiflage

I previously mentioned a problem concerning polynomials, whose motivation came from thinking about weight one forms and the inverse Galois problem for finite subgroups of \(\mathrm{GL}_2(\mathbf{C}).\) I still like the polynomial problem, but I realized that I was confused about … Continue reading →

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Prime divisors of polynomials

Posted on May 29, 2016 by Persiflage

A heuristic model from the last post suggests that the “expected” order of the Galois group associated to a weight one modular form of projective type \(A_5\) is infinite. And when one tries to solve the inverse Galois problem for … Continue reading →

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Inverse Galois Problems II

Posted on January 13, 2015 by Persiflage

David Zywina was in town today to talk about a follow up to his previous results mentioned previously on this blog. This time, he talked about his construction of Galois groups which were simple of orthogonal type, in particular, the … Continue reading →

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Inverse Galois Problem

Posted on April 24, 2013 by Persiflage

My favourite group as far as the inverse Galois problem goes is \(G = \mathrm{SL}_2(\mathbf{F}_p)\). This is not known to be a Galois group over \(\mathbf{Q}\) for any \(p > 13\), the difficulty of course being that is must correspond … Continue reading →

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