Tag Archives: Galois Representations

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

Scholze on Torsion, Part III

This is a continuation of Part I and Part II. Before I continue along to section V.3, I want to discuss an approach to the problem of constructing Galois representations from the pre-Scholze days. Let’s continue with the same notation … Continue reading

Posted in Mathematics | Tagged , , , , | 3 Comments

Scholze on Torsion, Part II

This is a sequel to Part I. Section V.1: Today we will talk about Chapter V. We will start with Theorem V.1.4. This is basically a summary of the construction of Galois representations in the RACSDC case, which follows, for … Continue reading

Posted in Mathematics | Tagged , , , , , | 6 Comments

Scholze on Torsion, Part I

This is a sequel to this post, although as it turns out we still won’t actually get to anything substantial — or indeed anything beyond an introduction — in this post. Let me begin with some overview. Suppose that is … Continue reading

Posted in Mathematics | Tagged , , , | 13 Comments