Tag Archives: Serre

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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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

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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

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Winning the Chocolate

Once a month, there is an (unrated) round robin blitz tournament at the Evanston chess club. The time controls are set on five minutes (a little slow for me, I usually play one minute games online), but it’s nice to … Continue reading

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