Timeline for Rank $2$ motivic local systems on a curve
Current License: CC BY-SA 4.0
4 events
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| Jan 30, 2023 at 2:13 | comment | added | naf | Thanks a lot for the reference! | |
| Jan 28, 2023 at 12:33 | comment | added | SashaP | This follows from the arguments for Theorem 5 and Corollary 4.9 in Simpson's numdam.org/article/PMIHES_1992__75__5_0.pdf The local system there is required to be rigid, but this is used only to conclude that it and all of its Galois conjugates admit a complex VHS, the property which is satisfied by motivic local system. The key point of the proof is that Griffiths transversality allows you to pin down the a priori arbitrary Hodge type of the VHS as having weights 0,0 or 0,1. One then applies the observation that a polarized Z-VHS of weights 0,1 comes from an abelian scheme. | |
| Jan 17, 2023 at 6:34 | history | edited | naf | CC BY-SA 4.0 |
added 253 characters in body; edited tags
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| Jan 16, 2023 at 4:36 | history | asked | naf | CC BY-SA 4.0 |