Tag Archives: Galois Representations

Dembélé on Abelian Surfaces with good reduction everywhere

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

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

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

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

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

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

Let be an arbitrary number field. Let be a prime which splits completely in , and consider an absolutely irreducible representation: which is unramified outside finitely many primes. If one assumes that is geometric, then the Fontaine–Mazur conjecture predicts that … Continue reading

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