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Tag Archives: RLT
A nonliftable weight one form modulo p^2
I once idly asked RLT (around 2004ish) whether one could use BuzzardTaylor arguments to prove that any representation: which was unramified at p and residually irreducible (and modular) was itself modular (in the Katz sense). Galois representations of this flavour … Continue reading
Serre 1: Calegari 0
I just spent a week or so trying to determine whether Serre’s conjecture about the congruence subgroup property was false for a very specific class of Sarithmetic groups. The punch line, perhaps not surprisingly, was that I had made an … Continue reading
Posted in Mathematics
Tagged Contradictions, CSP, Fred Diamond, Fred Diamond's Beard, George Boxer, Ihara's Lemma, John Voight, Keerthi, Mathematica, Matthew Emerton, Ribet, RLT, Serre
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Random Photos
Lunt Hall, the Northwestern mathematics building, recently underwent an upgrade of the fire alarm system. This includes introducing informative new signage, such as the following: Another change is that the “internal” window to my office was boarded up. The window … Continue reading
Posted in Waffle
Tagged Duke, Fire Alarm, Jonathan Wahl, Office Hours, Oracle at Delphi, RLT, Sarnak, TARDIS
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Harris 60
I’ve just returned from the excellent MSRI workshop which honored Michael Harris’ 60th birthday, and here is a brief summary of some of the gossip and mathematics I picked up when I was there. First, let me take note of … Continue reading
Posted in Mathematics, Uncategorized, Waffle
Tagged Akshay Venkatesh, Daniel Erman, David Geraghty, Kate Bekinsdale, Michael Harris, Patching, RLT, TaylorWiles
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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
Huuuuuge piles of cash
As widely reported today, the first of the “Breakthrough” prizes in mathematics have been announced. Leaving aside the question as to whether such awards are sensible (Persiflage is more sympathetic to capitalist principles than your average pinko marxist mathematician), I … Continue reading
Galois Representations for non selfdual forms, Part II
(Now with updates!) Let’s recap from part I. We have a Shimura variety , a minimal projective compactification , and a (family of) smooth toroidal compactifications . We also have Galois representations of the correct shape associated to eigenclasses in … Continue reading