Timeline for Companions for positive characteristic arithmetic representations viewed as representations of the topological fundamental group?
Current License: CC BY-SA 4.0
4 events
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| Jul 15 at 19:58 | comment | added | Ben C | @WillSawin, so suppose $\rho$ arises from some smooth proper morphism $f : Y \to X_{\bar{s}}$ then if I interpret what you are saying correctly, it is that in this case, my claim about the characteristic polynomials of $\rho|_{\pi}$ and $\rho^{\sigma}|_{\pi}$ is true. I don't see how to prove it, could you point me in the right direction? Thank you. Also could you elaborate on what sort of twist I need to do if $\rho$ is not irreducible? | |
| Jul 15 at 18:07 | comment | added | Will Sawin | If $\rho$ comes from a motive then the companions will all come from the motive and hence be isomorphic representations. Conjecturally $\rho$ comes from a motive(up to some twisting if $\rho$ is not geometrically irreducible) but there's no proof. | |
| Jul 15 at 16:44 | history | edited | Ben C | CC BY-SA 4.0 |
edited title
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| Jul 15 at 16:32 | history | asked | Ben C | CC BY-SA 4.0 |