Tag Archives: Kevin Buzzard

An Obvious Claim

Posted on July 6, 2014 by Persiflage

It’s been a while since I saw Serre’s “how to write mathematics badly” lecture, but I’m pretty sure there would have been something about the dangers of using the word “obvious.” After all, if something really is obvious, then it … Continue reading →

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

Are Galois deformation rings Cohen-Macaulay?

Posted on April 2, 2014 by Persiflage

Hyman Bass once wrote a paper on the ubiquity of Gorenstein rings. The first time they arose in the context of Hecke algebras, however, was Barry’s Eisenstein ideal paper, where he proves (at prime level) that the completions \(\mathbf{T}_{\mathfrak{m}}\) are … Continue reading →

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

Robert Coleman

Posted on March 25, 2014 by Persiflage

I was very sad to learn that, after a long illness with multiple sclerosis, Robert Coleman has just died. Robert’s influence on mathematics is certainly obvious to all of us in the field. Most of my personal interaction with him … Continue reading →

Posted in Uncategorized | Tagged , , | Leave a comment

Local crystalline deformation rings

Posted on February 8, 2014 by Persiflage

I just returned from a very pleasant conference in Puerto Rico courtesy of the Simons Foundation (general advice: if you live in Chicago, always accept invitations to conferences in January). One thing I learnt from Toby Gee was the following … Continue reading →

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

The mystery of the primes

Posted on January 4, 2014 by Persiflage

No, this is not the sequel to Marcus du Sautoy’s book, but rather a curious observation regarding George Schaeffer’s tables of “ethereal” weight one Katz modular eigenforms (which you can find starting on p.64 here). Let \(N\) be a positive … Continue reading →

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

Remarks on Buzzard-Taylor

Posted on October 18, 2012 by Persiflage

Let \(\rho: G_{\mathbf{Q},S} \rightarrow \mathrm{GL}_2(\overline{\mathbf{Q}}_p)\) be continuous and unramified at \(p\). The Fontaine-Mazur conjecture predicts that \(\rho\) has finite image and is automorphic. Buzzard and Taylor proved this result under the assumption the natural assumption that \(\rho\) is odd, that … Continue reading →

Posted in Mathematics | Tagged , , | Leave a comment