Tag Archives: Fontaine-Mazur Conjecture

A Brief Digest of Some New OpenAI Results

Posted on October 8, 2026 by Persiflage

I thought it might be worth discussing some of the recent OpenAI results in my field, or at least in algebraic number theory. For each of them, I’d like to offer a few thoughts, if I have any, on what … Continue reading →

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Unramified Fontaine-Mazur for representations coming from abelian varieties

Posted on May 9, 2024 by Persiflage

Mark Kisin gave a talk at the number theory seminar last week where the following problem arose: Let \(W\) be the Galois representation associated to the Tate module of an abelian variety \(A\) over a number field, and suppose that … Continue reading →

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A public service announcement concerning Fontaine-Mazur for GL(1)

Posted on July 12, 2014 by Persiflage

There’s a rumour going around that results from transcendence theory are required to prove the Fontaine-Mazur conjecture for \(\mathrm{GL}(1)\). This is not correct. In Serre’s book on \(\ell\)-adic representations, he defines a \(p\)-adic representation \(V\) of a global Galois group … Continue reading →

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