Seminar Announcement
Venue: CMI Seminar Hall (We plan to have it in hybrid mode)
Date: March 24, 2022, Thursday
Time: 3:30 pm to 4:30 pm
Trianguline property of Galois representations at the boundary of the eigencurve
Aditya Karnataki
BICMR, Peking University.
24-03-22

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Abstract

p-adic Langlands program aims to study and classify p-adic representations of the Galois group. The category of $(\varphi, \Gamma)$-modules constructed by Fontaine and others provides a highly useful tool to study such representations. When these representations arise from modular forms (more generally, their families parametrized by the eigencurve), the associated $(\varphi, \Gamma)$-modules satisfy a powerful and key property of being `trianguline'. Recent work by Andreatta-Iovita-Pilloni has made it possible to study new and mysterious families of modular forms at the boundary of the eigencurve. In this talk, we explain a proof of the conjecture that these forms at the boundary are Trianguline, too. This is joint work with Ruochuan Liu.