Tag Archives: Geraghty

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

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There are non-liftable weight one forms modulo p for any p

Let be any prime. In this post, we show that there is an integer prime to such that has a torsion class of order . Almost equivalently, there exists a Katz modular form of level and weight one over which … Continue reading

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A Preview of Barbados/Bellairs

This post is probably not so interesting unless you plan to travel to the Caribbean in a few weeks. The website for the conference is offline, so I thought I might update attendees on what might be happening, at least … Continue reading

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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

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Scholze on Torsion 0

This will be the first zeroth of a series of posts talking about Scholze’s recent preprint, available here. This is mathematics which will, no question, have more impact in number theory than any recent paper I can think of. The … Continue reading

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Finiteness of the global deformation ring over local deformation rings

(This post is the result of a conversation I had with Matt). Suppose that is a continuous mod- absolutely irreducible Galois representation. For now, let’s assume that is a CM field, and is essentially self-dual and odd. Associated to this … Continue reading

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