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SUMMARY:Lue Pan (University of Chicago)
DTSTART:20201124T213000Z
DTEND:20201124T223000Z
DTSTAMP:20260423T130123Z
UID:MITNT/19
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITNT/19/">O
 n the locally analytic vectors of the completed cohomology of modular curv
 es</a>\nby Lue Pan (University of Chicago) as part of MIT number theory se
 minar\n\n\nAbstract\nA classical result identifies holomorphic modular for
 ms with\nhighest weight vectors of certain representations of $SL_2(\\math
 bb{R})$. We\nstudy locally analytic vectors of the (p-adically) completed 
 cohomology of\nmodular curves and prove a p-adic analogue of this result. 
 As\napplications\, we are able to prove a classicality result for\novercon
 vergent eigenforms and give a new proof of Fontaine-Mazur\nconjecture in t
 he irregular case under some mild hypothesis. One technical\ntool is relat
 ive Sen theory which allows us to relate infinitesimal group\naction with 
 Hodge(-Tate) structure.\n
LOCATION:https://researchseminars.org/talk/MITNT/19/
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