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SUMMARY:Andrew Graham (Université Paris-Saclay)
DTSTART:20221201T173000Z
DTEND:20221201T190000Z
DTSTAMP:20260423T023936Z
UID:UCSBsga/40
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UCSBsga/40/"
 >A unipotent circle action on nearly overconvergent modular forms</a>\nby 
 Andrew Graham (Université Paris-Saclay) as part of UCSB Seminar on Geomet
 ry and Arithmetic\n\n\nAbstract\nRecent work of Howe shows that the action
  of the Atkin--Serre operator on p-adic modular forms can be reinterpreted
  as a $\\widehat{\\mathbb{G}}_m$ action on the Katz Igusa tower. By p-adic
  Fourier theory\, this gives an action of continuous functions on $\\mathb
 b{Z}_p$ on sections of the Igusa tower (p-adic modular forms). In this tal
 k I will explain how one can ``overconverge'' this action\, i.e. show that
  the subspace of nearly overconvergent modular forms is stable under the a
 ction of locally analytic functions on $\\mathbb{Z}_p$. This recovers (but
  is more general than) the construction of Andreatta--Iovita and has appli
 cations to the construction of p-adic L-functions. (Joint work with Vincen
 t Pilloni and Joaquin Rodrigues).\n
LOCATION:https://researchseminars.org/talk/UCSBsga/40/
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