Fontaine–Mazur modularity at the prime 2
We prove that every continuous, irreducible, odd two-dimensional 2-adic representation of $G_{\mathbb Q}$, unramified outside finitely many primes and de Rham at 2 with distinct Hodge–Tate weights, is modular up to Tate twist. This resolves the odd, regular two-dimensional Fontaine–Mazur conjecture over ℚ at 2, including all residual representations.
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A Brief Digest of Some New OpenAI Results | Persiflagegaloisrepresentations.orgPersiflage
It is very clean, which is useful for applications. That said, upon closer inspection this paper may turn out to have some really clever new trick, but I can’t see what that is on a superficial reading. I would actually say I’m surprised that this is a problem OpenAI would have tried to solve,…