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Meta
Tag Archives: Galois Representations
The horizontal Breuil-Mezard conjecture
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
Posted in Mathematics, Students, Work of my students
Tagged Andreea Iorga, Andrew Wiles, Ariane Mézard, Breuil-Mezard, Chengyang Bao, Christophe Breuil, Cohen-Macaulay, Galois Representations, Gorenstein, Hilbert, Hiring Season, Kevin Buzzard, Local Langlands, Mark Kisin, Richard Taylor, Sandra Rozensztajn, Taylor-Wiles, Toby Gee
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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
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
Posted in Uncategorized
Tagged Eigencurve, Galois Representations, Halo, Kevin Buzzard, Lloyd Kilford, OPAQUE, Robert Coleman
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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
Posted in Uncategorized
Tagged Artin Conjecture, Galois Representations, Hodge-Tate, lifting, On the record
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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
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
Posted in Mathematics
Tagged Abandonware, Akshay Venkatesh, Andrew Odlyzko, Bernard Woolley, David Geraghty, Dick Gross, Discriminant Bounds, Galois Representations, Imaginary Quadratic Fields, Jacquet-Langlands, John Voight, Lassina Dembélé, Matthew Greenberg, Peter Sarnak, Publishing, Taylor-Wiles, Under The Cosh, Yes Minister
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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
The nearly ordinary deformation ring is (usually) torsion over weight space
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
Is Serre’s conjecture still open?
The conjecture in this paper has indeed been proven. But that isn’t the entire story. Serre was fully aware of Katz modular forms of weight one. However, Serre was too timid was prudently conservative and made his conjecture only for … Continue reading