Timeline for Can Frobenius traces jump like crazy in non-geometric Galois representations?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 25, 2021 at 10:26 | comment | added | David Loeffler | Chebotarev density shows that the Frobenius conj classes are uniformly distributed in the l-adic topology -- this is far easier than Sato-Tate and geometricity is not required | |
| Sep 25, 2021 at 8:58 | comment | added | Mellic | When you say "random" can that be made more precise? Is there a conjecture like Sato-Tate for non-geometric representations? | |
| Sep 25, 2021 at 7:57 | comment | added | David Loeffler | All traces will be $\ell$-adically integral, and they'll behave like the trace of a random conjugacy class in $\operatorname{Im}(\rho)$, which is some irreducible subgroup of $\operatorname{GL}_n$. But that's not terribly deep and it's hard to say more than that. | |
| Sep 25, 2021 at 7:56 | history | edited | David Loeffler | CC BY-SA 4.0 |
fixed $\ell$ vs $p$
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| Sep 25, 2021 at 7:51 | comment | added | Mellic | If we drop the assumption about algebraicity can anything be said about the $l$-valuation of the traces? | |
| Sep 25, 2021 at 7:25 | history | answered | David Loeffler | CC BY-SA 4.0 |