YoVDO

Multivariable (φ, Γ)-Modules and Local-Global Compatibility

Offered By: BIMSA via YouTube

Tags

Galois Representations Courses Algebraic Number Theory Courses

Course Description

Overview

Save Big on Coursera Plus. 7,000+ courses at $160 off. Limited Time Only!
Explore the intricacies of multivariable $(\varphi, \Gamma)$-modules and their connection to local-global compatibility in this 54-minute lecture by Yongquan Hu at BIMSA. Delve into the generalization of Colmez's construction, associating admissible smooth mod $p$ representations of $\mathrm{GL}_2(K)$ with multivariable (étale) $(\varphi, \mathcal{O}_K^{\times})$-modules over a suitable ring $A$. Examine the challenges in explicitly computing these modules and discover how they can be calculated when derived from Hecke eigenspaces in mod $p$ cohomology of Shimura curves. Compare the results with multivariable $(\varphi, \mathcal{O}_K^{\times})$-modules associated with mod $p$ Galois representations. Gain insights into this collaborative research effort with Breuil, Herzig, Morra, and Schraen, advancing our understanding of local-global compatibility in number theory.

Syllabus

Yongquan Hu: Multivariable $(\varphi, \Gamma)$-modules and local-global compatibility #ICBS2024


Taught by

BIMSA

Related Courses

Exceptional Splitting of Reductions of Abelian Surfaces With Real Multiplication - Yunqing Tang
Institute for Advanced Study via YouTube
A Derived Hecke Algebra in the Context of the Mod P Langlands Program - Rachel Ollivier
Institute for Advanced Study via YouTube
Arithmetic Statistics and the Iwasawa Theory of Elliptic Curves
Fields Institute via YouTube
Jacob Lurie: A Riemann-Hilbert Correspondence in p-adic Geometry
Hausdorff Center for Mathematics via YouTube
Panorama of Mathematics - Peter Scholze
Hausdorff Center for Mathematics via YouTube