Tag Archives: Galois Representations

It’s not a Lemma, it’s a Proposition!

Posted on December 14, 2024 by Persiflage

Congratulations to Ken for winning the the Steele prize. I first met Ken on the Hearst mining circle. It was September of 1997, during the time I was applying for graduate schools. I was visiting Danny on the way to … Continue reading →

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The horizontal Breuil-Mezard conjecture

Posted on October 19, 2023 by Persiflage

Postdoc hiring season will be upon us soon! I have two excellent graduate students who will be applying for academic jobs soon, Chengyang Bao and Andreea Iorga. I have mentioned Chengyang’s first project before here and an introduction to the … Continue reading →

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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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A strange continuity

Posted on November 25, 2018 by Persiflage

Returning to matters OPAQUE, here is the following problem which may well now be approachable by known methods. Let me phrase the conjecture in the case when the prime p = 2 and the level N = 1. As we … Continue reading →

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Irregular Lifts, Part II

Posted on October 28, 2018 by Persiflage

This is the global counterpart to the last post. I was going to write this post in a more general setting, but the annoyances of general reductive groups got the better of me. Suppose we fix the following: A number … Continue reading →

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Irregular Lifts, Part I

Posted on October 19, 2018 by Persiflage

This post motivated in part by the recent preprint of Fakhruddin, Khare, and Patrikis, and also by Matt’s number theory seminar at Chicago this week. (If you are interested in knowing what the calendar is for the Chicago number theory … Continue reading →

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Abandonware

Posted on December 25, 2017 by Persiflage

For a young mathematician, there is a lot of pressure to publish (or perish). The role of for-profit academic publishing is to publish large amounts of crappy mathematics papers, make a lot of money, but at least in return grant … Continue reading →

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Report From Berkeley

Posted on April 22, 2016 by Persiflage

My recent trip to Berkeley did not result in a chance to test whether the Cheeseboard pizza maintained its ranking, but did give me the opportunity to attend the latest Bay Area Number Theory and Algebraic Geometry day, on a … Continue reading →

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The nearly ordinary deformation ring is (usually) torsion over weight space

Posted on September 19, 2014 by Persiflage

Let \(F/{\mathbf{Q}}\) be an arbitrary number field. Let \(p\) be a prime which splits completely in \(F\), and consider an absolutely irreducible representation: \(\rho: G_{F} \rightarrow {\mathrm{GL}}_2({\overline{\mathbf{Q}}}_p)\) which is unramified outside finitely many primes. If one assumes that \(\rho\) is … Continue reading →

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