Timeline for On Fourier coefficients of Bianchi modular forms, l-ordinary
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Apr 14, 2021 at 8:45 | comment | added | David Loeffler | I think this might be a bit more delicate than it looks. The argument of Serre is based on bounding how often we can have $a_\ell(f) = 0$. If the coefficient field is $\mathbf{Q}$ then it follows from the Hasse--Weil bound that $\ell$ can only divide $a_\ell(f)$ if it is zero, but this breaks down if the coefficient field is larger. The argument of Hida applies to the case when the form is for $GL2/K$ and the coeff field is equal to K, and shows only that there is a density 1 set of primes $\ell$ for which $f$ is ordinary at some prime above $\ell$ ("partially ordinary" in Hida's notation). | |
| Apr 13, 2021 at 15:32 | comment | added | Kimball | Crossposted from MSE: math.stackexchange.com/q/4100189/11323 | |
| Apr 13, 2021 at 11:04 | comment | added | Ariel Weiss | I think this should be known (assuming of course that $f$ is not a theta lift, in which case it's false). Prop. 2.2 of the Fischman paper quotes Thm 15 this Serre paper. The only modular forms specific input of the proof is Prop 17, which requires knowing that the $l$-adic Galois representation $G_K \to \mathrm{GL}_2(\overline{\mathbb Q}_\ell)$ associated to $f$ is absolutely irreducible when restricted to any finite extension of $K$. But this is known for Bianchi modular forms. | |
| Apr 13, 2021 at 5:57 | history | edited | Francesco Polizzi | CC BY-SA 4.0 |
added 21 characters in body
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| Apr 13, 2021 at 3:41 | review | First posts | |||
| Apr 13, 2021 at 5:46 | |||||
| Apr 13, 2021 at 3:38 | history | asked | jason kwon | CC BY-SA 4.0 |