Tag Archives: Galois Representations

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 , , , , , , , , , , , , , , , , , | 4 Comments

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

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

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

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

Posted in Mathematics | Tagged , , , , , , , , , , , , , | 2 Comments

A public service announcement concerning Fontaine-Mazur for GL(1)

There’s a rumour going around that results from transcendence theory are required to prove the Fontaine-Mazur conjecture for . This is not correct. In Serre’s book on -adic representations, he defines a -adic representation of a global Galois group to … Continue reading

Posted in Mathematics | Tagged , , , | 2 Comments

Report from Luminy

For how long has Luminy been infested with bloodthirsty mosquitoes? The combination of mosquitoes in my room with the fact that my bed was 6′ long with a completely unnecessary headboard (which meant that I had to sleep on an … Continue reading

Posted in Mathematics, Uncategorized | Tagged , , , , , , , | 5 Comments

Scholze on Torsion, Part IV

This is a continuation of Part I, Part II, and Part III. I was planning to start talking about Chapter IV, instead, this will be a very soft introduction to a few lines on page 72. At this point, we … Continue reading

Posted in Mathematics | Tagged , , , , , , , , , , | 2 Comments