Tag Archives: Serre

Correspondance Serre-Tate, Part I

Reading the correspondence between Serre and Tate has been as delightful as one could expect. What is very nice to see — although perhaps not so surprising — is the utter delight that both Serre and Tate find in discussing … Continue reading

Posted in Mathematics | Tagged , , , , , , , , , , , , , , | 4 Comments

Indulgences

Today is Persiflage’s birthday, but let us not also forget to wish many happy returns to friends of the blog Ana and Vytas, who share the same birthday! Here is how I plan to celebrate: I will┬áspare you with the … Continue reading

Posted in Food | Tagged , , , , , , , , , , , , , , , , , , , | 1 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

Ventotene, Part II

I promised to return to a more mathematical summary of the conference in Ventotene, and indeed I shall do so in the next two posts. One of the themes of the conference was bounding the order of the torsion subgroup … Continue reading

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

Review of Buzzard-Gee

This is a review of the paper “Slopes of Modular Forms” submitted for publication in a Simons symposium proceedings volume. tl;dr: This paper is a nice survey article on questions concerning the slopes of modular forms. Buzzard has given a … Continue reading

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

Derived Langlands

Although it has been in the air for some time, it seems as though ideas from derived algebraic geometry have begun to inform developments in the Langlands program. (A necessary qualifier: I am talking about reciprocity in the classical arithmetic … 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