Timeline for $\ell$-adic analogue of Kedlaya-Mochizuki
Current License: CC BY-SA 4.0
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| 4 hours ago | comment | added | Will Sawin | @Gabriel I don't see any difference between the exponential connection of a rational function and the exponential section of a meromorphic function in this context. (We're working locally, a meromorphic function is locally a rational function plus a holomorphic function, and the exponential connection of a holomorphic function is locally trivial). The issue is that $p$-dimensional irreducible representations of the wild inertia group are not like any kind of exponential connection, since they are $p$-dimensional and exponential connections are $1$-dimensional. | |
| 4 hours ago | comment | added | Gabriel | Hi Will! Instead of generalizing this result to higher dimensions, do you have any idea on how to generalize it to higher-rank sheaves on curves? Very naively, I imagine that one should generalize the Artin-Schreier-Witt sheaves to something akin to the exponential connection of a meromorphic function. | |
| 7 hours ago | history | answered | Will Sawin | CC BY-SA 4.0 |