Morningside Center of Mathematics
Chinese Academy of Sciences
Morningside Center of Mathematics
Chinese Academy of Sciences
| Title: | On the locally analytic vectors of the completed cohomology of modular curves I: Main results |
| Speaker: | Lue Pan (University of Chicago) |
| Time: | 2020-9-10, 9:30-10:30 |
| Place: | ZOOM;ID:4663562952;Pswd:mcm1234 |
| Abstract: | We study locally analytic vectors of the completed cohomology of modular curves and determine eigenvectors of a rational Borel subalgebra of gl_2(Q_p). As applications, we are able to prove a classicality result for overconvergent eigenform of weight one and give a new proof of Fontaine-Mazur conjecture in the irregular case under some mild hypothesis. One technical tool is relative Sen theory which allows us to relate infinitesimal group action with Hodge(-Tate) structure. |
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