Tag Archives: RLT

A non-liftable weight one form modulo p^2

I once idly asked RLT (around 2004ish) whether one could use Buzzard-Taylor 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

Posted in Mathematics | Tagged , , , | Leave a comment

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 S-arithmetic groups. The punch line, perhaps not surprisingly, was that I had made an … Continue reading

Posted in Mathematics | Tagged , , , , , , , , , , , , | Leave a comment

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 , , , , , , , | Leave a comment

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 , , , , , , , | 2 Comments

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

Posted in Mathematics | Tagged , , , | Leave a comment

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

Posted in Mathematics, Politics | Tagged , | 4 Comments

Galois Representations for non self-dual 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

Posted in Mathematics | Tagged , , , , | 1 Comment