Multivariable (phi, Gamma)-modules and modular representations of Galois and GL2

Abstract: Let \(p\) be a prime number, \(K\) a finite unramified extension of \(\mathbf{Q}_p\), and \(\pi\) a smooth representation of \(\mathrm{GL}_2(K)\) on some Hecke eigenspace in the \(H^1\) mod \(p\) of a Shimura curve. One can associate to \(\pi\) a multivariable \( (\phi, O_K^*)\)-module \(D_A(\pi) \). I will state a conjecture which describes \( D_A(\pi) \) in terms of the underlying 2-dimensional mod \(p\) representation of \(\mathrm{Gal}(\bar{K}/K)\). When the latter is semi-simple (sufficiently generic), I will sketch a proof of this conjecture. This is joint work with F. Herzig, Y. Hu, S. Morra and B. Schraen.

algebraic geometrynumber theoryrepresentation theory

Audience: researchers in the topic

Comments: Zoom number: 743 736 2326

Zoom password: 013049

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POINTS - Peking Online International Number Theory Seminar

Series comments: Description: Seminar on number theory and related topics

This seminar series is sponsored by the Beijing International Center of Mathematical Research (BICMR) and the School of Mathematical Sciences of Peking University.

The conference number and password are available on the external website. See also the announcements on bicmr.pku.edu.cn

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