Timeline for Galois action on the cohomology of a curve over a local field with bad reduction
Current License: CC BY-SA 4.0
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| Sep 19 at 16:04 | comment | added | Asvin | @JamesRawson thanks! That exact sequence is almost exactly what I want. I am also interested in what happens away from the inertia invariant locus. By analogy with the elliptic curve case + a dimension count, I think I can guess what happens (the frobenius lift should act by a scalar p after you quotient out the inertia invariants, and the dim is the dimension of H1 of the dual graph) but it would be great to have a reference to confirm it. Thanks anyway, I think this basically answers my mathematical question. | |
| Sep 19 at 9:20 | comment | added | James Rawson | In Adam Morgan's notes ( heilbronn.ac.uk/wp-content/uploads/2018/09/adam-morgan.pdf ) lecture 4, there is a description of the Tate module (for $\ell \neq p$) in terms of a short exact sequence, and the terms of which correspond to the components. | |
| Sep 19 at 6:36 | history | asked | Asvin | CC BY-SA 4.0 |