On the locally analytic vectors of the completed cohomology of modular curves
Lue Pan (University of Chicago)
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.
commutative algebraalgebraic geometrynumber theory
Audience: researchers in the topic
Recent Advances in Modern p-Adic Geometry (RAMpAGe)
Series comments: The Zoom Meeting ID is: 995 3670 1681. The password for the series is: *The first three-digit prime*. Please visit the external homepage for notes and videos from past talks.
Organizers: | David Hansen*, Arthur-César Le Bras*, Jared Weinstein* |
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