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Tag Archives: Langlands
LMFDB!?
The LMFDB has gone live! I previously expressed on this blog a somewhat muted opinion about certain aspects of the website’s functionality, and it seems that my complaints have mainly been addressed in the latest version. On the other hand, … Continue reading
Posted in Mathematics, Rant
Tagged Cremona, Cris Poor, David Yuen, John Voight, Langlands
31 Comments
Review of BuzzardGee
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
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 Akshay Venkatesh, DAG, Derived Algebraic Geometry, Derived Langlands, Geraghty, Gillet, Langlands, Roberts, Serre, Soule
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The Artin conjecture is rubbish
Let be a continuous irreducible representation. Artin conjectured that the Lfunction is analytically continues to an entire function on (except for the trivial representation where the is a simple pole at one) and satisfies a functional equation of a precise … Continue reading
Posted in Mathematics
Tagged Andrew Booker, Artin, Cebotarev Density Theorem, Class Number Problem, Goldfeld, GRH, Gross, Jo Dwyer, Langlands, Rubbish, Springer, Stark, Zagier
9 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 Emerton, Fargues, Galois Representations, Geraghty, Langlands, Mantovan, Reduzzi, Scholze, torsion, Weinstein, Xiao
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 preScholze days. Let’s continue with the same notation … Continue reading
Posted in Mathematics
Tagged Galois Representations, Langlands, Scholze, torsion, Vaporware
1 Comment
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