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SUMMARY:Juan Esteban Rodriguez Camargo (ENS de Lyon)
DTSTART:20210210T160000Z
DTEND:20210210T170000Z
DTSTAMP:20260418T064529Z
UID:LNTS/28
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LNTS/28/">Du
 al Eichler-Shimura maps for the modular curve</a>\nby Juan Esteban Rodrigu
 ez Camargo (ENS de Lyon) as part of London number theory seminar\n\n\nAbst
 ract\nAndreatta-Iovita-Stevens  have  constructed interpolations of the sm
 all slope part of the Eichler-Shimura decomposition for the modular curve.
  Roughly speaking\, they defined in a geometric way a map from the overcon
 vergent modular symbols of weight k\, to the overconvergent modular forms 
 of weight k+2. Then\, using classicality theorems of  Coleman and  Ash-Ste
 vens\, they achieved a Hodge-Tate decomposition of the small slope part of
  overconvergent modular symbols. On the other hand\, in a recent paper of 
 Boxer-Pilloni\, the authors  proved that higher Coleman and Hida theories 
 exist for the modular curve. The aim of this talk is to construct geometri
 cally a map from the higher cohomology of  overconvergent modular forms of
  weight -k to the modular symbols as above. We shall recover the Hodge-Tat
 e decomposition of the small slope part of modular symbols\, with the addi
 tion that all the maps involved are defined using the geometry of the modu
 lar curve. If time permits\, we will discuss the compatibility of the prev
 ious work with duality.\n
LOCATION:https://researchseminars.org/talk/LNTS/28/
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